Power Algebras over Semirings: With Applications in Mathematics and Computer Science
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | Mathematics and Its Applications
488 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light |
| Beschreibung: | 1 Online-Ressource (X, 206 p) |
| ISBN: | 9789401592413 9789048152704 |
| DOI: | 10.1007/978-94-015-9241-3 |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9241-3 |
| format | Electronic eBook |
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| isbn | 9789401592413 9789048152704 |
| language | English |
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| spelling | Golan, Jonathan S. Verfasser aut Power Algebras over Semirings With Applications in Mathematics and Computer Science by Jonathan S. Golan Dordrecht Springer Netherlands 1999 1 Online-Ressource (X, 206 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 488 This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light Mathematics Computational complexity Algebra Logic, Symbolic and mathematical Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Discrete Mathematics in Computer Science Mathematical Logic and Foundations Mathematik Halbring (DE-588)4123331-1 gnd rswk-swf Halbring (DE-588)4123331-1 s 1\p DE-604 https://doi.org/10.1007/978-94-015-9241-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Golan, Jonathan S. Power Algebras over Semirings With Applications in Mathematics and Computer Science Mathematics Computational complexity Algebra Logic, Symbolic and mathematical Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Discrete Mathematics in Computer Science Mathematical Logic and Foundations Mathematik Halbring (DE-588)4123331-1 gnd |
| subject_GND | (DE-588)4123331-1 |
| title | Power Algebras over Semirings With Applications in Mathematics and Computer Science |
| title_auth | Power Algebras over Semirings With Applications in Mathematics and Computer Science |
| title_exact_search | Power Algebras over Semirings With Applications in Mathematics and Computer Science |
| title_full | Power Algebras over Semirings With Applications in Mathematics and Computer Science by Jonathan S. Golan |
| title_fullStr | Power Algebras over Semirings With Applications in Mathematics and Computer Science by Jonathan S. Golan |
| title_full_unstemmed | Power Algebras over Semirings With Applications in Mathematics and Computer Science by Jonathan S. Golan |
| title_short | Power Algebras over Semirings |
| title_sort | power algebras over semirings with applications in mathematics and computer science |
| title_sub | With Applications in Mathematics and Computer Science |
| topic | Mathematics Computational complexity Algebra Logic, Symbolic and mathematical Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Discrete Mathematics in Computer Science Mathematical Logic and Foundations Mathematik Halbring (DE-588)4123331-1 gnd |
| topic_facet | Mathematics Computational complexity Algebra Logic, Symbolic and mathematical Associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Discrete Mathematics in Computer Science Mathematical Logic and Foundations Mathematik Halbring |
| url | https://doi.org/10.1007/978-94-015-9241-3 |
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