Algebraic Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973
|
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
192 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic principles of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abundant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra |
| Beschreibung: | 1 Online-Ressource (XII, 320 p) |
| ISBN: | 9783642653742 9783642653766 |
| DOI: | 10.1007/978-3-642-65374-2 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042422871 | ||
| 003 | DE-604 | ||
| 005 | 20240626 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1973 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642653742 |c Online |9 978-3-642-65374-2 | ||
| 020 | |a 9783642653766 |c Print |9 978-3-642-65376-6 | ||
| 024 | 7 | |a 10.1007/978-3-642-65374-2 |2 doi | |
| 035 | |a (OCoLC)1165545515 | ||
| 035 | |a (DE-599)BVBBV042422871 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Mal'cev, A. I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic Systems |c by A. I. Mal'cev |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1973 | |
| 300 | |a 1 Online-Ressource (XII, 320 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |v 192 | |
| 500 | |a As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic principles of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abundant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Struktur |0 (DE-588)4001166-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Struktur |0 (DE-588)4001166-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 830 | 0 | |a Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |v 192 |w (DE-604)BV049758308 |9 192 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-65374-2 |x Verlag |3 Volltext |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
Datensatz im Suchindex
| _version_ | 1805079046318456832 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Mal'cev, A. I. |
| author_facet | Mal'cev, A. I. |
| author_role | aut |
| author_sort | Mal'cev, A. I. |
| author_variant | a i m ai aim |
| building | Verbundindex |
| bvnumber | BV042422871 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165545515 (DE-599)BVBBV042422871 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-65374-2 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nmm a2200000zcb4500</leader><controlfield tag="001">BV042422871</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240626</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1973 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642653742</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-65374-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642653766</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-65376-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-65374-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165545515</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422871</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mal'cev, A. I.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic Systems</subfield><subfield code="c">by A. I. Mal'cev</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1973</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XII, 320 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete</subfield><subfield code="v">192</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic principles of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abundant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Struktur</subfield><subfield code="0">(DE-588)4001166-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Struktur</subfield><subfield code="0">(DE-588)4001166-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete</subfield><subfield code="v">192</subfield><subfield code="w">(DE-604)BV049758308</subfield><subfield code="9">192</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-65374-2</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield></record></collection> |
| id | DE-604.BV042422871 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:38:45Z |
| institution | BVB |
| isbn | 9783642653742 9783642653766 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858288 |
| oclc_num | 1165545515 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XII, 320 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| series2 | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Mal'cev, A. I. Verfasser aut Algebraic Systems by A. I. Mal'cev Berlin, Heidelberg Springer Berlin Heidelberg 1973 1 Online-Ressource (XII, 320 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 192 As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic principles of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abundant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra Mathematics Mathematics, general Mathematik Algebra (DE-588)4001156-2 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 s 1\p DE-604 Algebra (DE-588)4001156-2 s 2\p DE-604 Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 192 (DE-604)BV049758308 192 https://doi.org/10.1007/978-3-642-65374-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mal'cev, A. I. Algebraic Systems Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete Mathematics Mathematics, general Mathematik Algebra (DE-588)4001156-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4001166-5 |
| title | Algebraic Systems |
| title_auth | Algebraic Systems |
| title_exact_search | Algebraic Systems |
| title_full | Algebraic Systems by A. I. Mal'cev |
| title_fullStr | Algebraic Systems by A. I. Mal'cev |
| title_full_unstemmed | Algebraic Systems by A. I. Mal'cev |
| title_short | Algebraic Systems |
| title_sort | algebraic systems |
| topic | Mathematics Mathematics, general Mathematik Algebra (DE-588)4001156-2 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Algebra Algebraische Struktur |
| url | https://doi.org/10.1007/978-3-642-65374-2 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT malcevai algebraicsystems |