The Theory of Partial Algebraic Operations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
414 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Nowadays algebra is understood basically as the general theory of algebraic operations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds application at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation |
| Beschreibung: | 1 Online-Ressource (X, 238 p) |
| ISBN: | 9789401734837 9789048148677 |
| DOI: | 10.1007/978-94-017-3483-7 |
Internformat
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| 500 | |a Nowadays algebra is understood basically as the general theory of algebraic operations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds application at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation | ||
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Datensatz im Suchindex
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-3483-7 |
| format | Electronic eBook |
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| id | DE-604.BV042424324 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401734837 9789048148677 |
| language | English |
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| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Ljapin, E. S. Verfasser aut The Theory of Partial Algebraic Operations by E. S. Ljapin, A. E. Evseev Dordrecht Springer Netherlands 1997 1 Online-Ressource (X, 238 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 414 Nowadays algebra is understood basically as the general theory of algebraic operations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds application at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation Mathematics Coding theory Group theory Algebra Functional analysis Logic, Symbolic and mathematical Mathematical Logic and Foundations Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Functional Analysis Coding and Information Theory Mathematik Evseev, A. E. Sonstige oth Mathematics and Its Applications 414 (DE-604)BV008163334 414 https://doi.org/10.1007/978-94-017-3483-7 Verlag Volltext |
| spellingShingle | Ljapin, E. S. The Theory of Partial Algebraic Operations Mathematics and Its Applications Mathematics Coding theory Group theory Algebra Functional analysis Logic, Symbolic and mathematical Mathematical Logic and Foundations Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Functional Analysis Coding and Information Theory Mathematik |
| title | The Theory of Partial Algebraic Operations |
| title_auth | The Theory of Partial Algebraic Operations |
| title_exact_search | The Theory of Partial Algebraic Operations |
| title_full | The Theory of Partial Algebraic Operations by E. S. Ljapin, A. E. Evseev |
| title_fullStr | The Theory of Partial Algebraic Operations by E. S. Ljapin, A. E. Evseev |
| title_full_unstemmed | The Theory of Partial Algebraic Operations by E. S. Ljapin, A. E. Evseev |
| title_short | The Theory of Partial Algebraic Operations |
| title_sort | the theory of partial algebraic operations |
| topic | Mathematics Coding theory Group theory Algebra Functional analysis Logic, Symbolic and mathematical Mathematical Logic and Foundations Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Functional Analysis Coding and Information Theory Mathematik |
| topic_facet | Mathematics Coding theory Group theory Algebra Functional analysis Logic, Symbolic and mathematical Mathematical Logic and Foundations Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Functional Analysis Coding and Information Theory Mathematik |
| url | https://doi.org/10.1007/978-94-017-3483-7 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT ljapines thetheoryofpartialalgebraicoperations AT evseevae thetheoryofpartialalgebraicoperations |