Polynomial Identity Rings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
2004
|
| Series: | Advanced Courses in Mathematics CRM Barcelona
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx). "Satisfying a polynomial identity" is often regarded as a generalization of commutativity. These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject. The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory |
| Physical Description: | 1 Online-Ressource (VII, 200 p) |
| ISBN: | 9783034879347 9783764371265 |
| DOI: | 10.1007/978-3-0348-7934-7 |
Staff View
MARC
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Record in the Search Index
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7934-7 |
| format | Electronic eBook |
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| id | DE-604.BV042421991 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034879347 9783764371265 |
| language | English |
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| spelling | Drensky, Vesselin Verfasser aut Polynomial Identity Rings by Vesselin Drensky, Edward Formanek Basel Birkhäuser Basel 2004 1 Online-Ressource (VII, 200 p) txt rdacontent c rdamedia cr rdacarrier Advanced Courses in Mathematics CRM Barcelona A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx). "Satisfying a polynomial identity" is often regarded as a generalization of commutativity. These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject. The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory Mathematics Algebra Combinatorics Associative Rings and Algebras Mathematik Polynomidentität (DE-588)4297308-9 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf PI-Algebra (DE-588)4309236-6 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s Polynomidentität (DE-588)4297308-9 s 1\p DE-604 PI-Algebra (DE-588)4309236-6 s 2\p DE-604 Formanek, Edward Sonstige oth https://doi.org/10.1007/978-3-0348-7934-7 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 | Drensky, Vesselin Polynomial Identity Rings Mathematics Algebra Combinatorics Associative Rings and Algebras Mathematik Polynomidentität (DE-588)4297308-9 gnd Ring Mathematik (DE-588)4128084-2 gnd PI-Algebra (DE-588)4309236-6 gnd |
| subject_GND | (DE-588)4297308-9 (DE-588)4128084-2 (DE-588)4309236-6 |
| title | Polynomial Identity Rings |
| title_auth | Polynomial Identity Rings |
| title_exact_search | Polynomial Identity Rings |
| title_full | Polynomial Identity Rings by Vesselin Drensky, Edward Formanek |
| title_fullStr | Polynomial Identity Rings by Vesselin Drensky, Edward Formanek |
| title_full_unstemmed | Polynomial Identity Rings by Vesselin Drensky, Edward Formanek |
| title_short | Polynomial Identity Rings |
| title_sort | polynomial identity rings |
| topic | Mathematics Algebra Combinatorics Associative Rings and Algebras Mathematik Polynomidentität (DE-588)4297308-9 gnd Ring Mathematik (DE-588)4128084-2 gnd PI-Algebra (DE-588)4309236-6 gnd |
| topic_facet | Mathematics Algebra Combinatorics Associative Rings and Algebras Mathematik Polynomidentität Ring Mathematik PI-Algebra |
| url | https://doi.org/10.1007/978-3-0348-7934-7 |
| work_keys_str_mv | AT drenskyvesselin polynomialidentityrings AT formanekedward polynomialidentityrings |