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Catalogue Information
Field name	Details
Dewey Class	512.46
Title	Polynomial Identity Rings ([EBook] /) / by Vesselin Drensky, Edward Formanek.
Author	Drensky, Vesselin
Added Personal Name	Formanek, Edward author.
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2004.
Physical Details	VII, 200 p. : online resource.
Series	Advanced courses in mathematics, CRM Barcelona
ISBN	9783034879347
Summary Note	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.:
Contents note	A Combinatorial Aspects in PI-Rings -- Vesselin Drensky -- 1 Basic Properties of PI-algebras -- 2 Quantitative Approach to PI-algebras -- 3 The Amitsur-Levitzki Theorem -- 4 Central Polynomials for Matrices -- 5 Invariant Theory of Matrices -- 6 The Nagata-Higman Theorem -- 7 The Shirshov Theorem for Finitely Generated PI-algebras -- 8 Growth of Codimensions of PI-algebras -- B Polynomial Identity Rings -- Edward Formanek -- 1 Polynomial Identities -- 2 The Amitsur-Levitzki Theorem -- 3 Central Polynomials -- 4 Kaplansky’s Theorem -- 5 Theorems of Amitsur and Levitzki on Radicals -- 6 Posner’s Theorem -- 7 Every PI-ring Satisfies a Power of the Standard Identity -- 8 Azumaya Algebras -- 9 Artin’s Theorem -- 10 Chain Conditions -- 11 Hilbert and Jacobson PI-Rings -- 12 The Ring of Generic Matrices -- 13 The Generic Division Ring of Two 2 x 2 Generic Matrices -- 14 The Center of the Generic Division Ring -- 15 Is the Center of the Generic Division Ring a Rational Function Field?.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-7934-7
Links to Related Works	Subject References: Associative rings . Associative Rings and Algebras . Combinatorics . Mathematics . Rings (Algebra) . Authors: Drensky, Vesselin . Formanek, Edward . Corporate Authors: SpringerLink (Online service) . Series: Advanced courses in mathematics, CRM Barcelona . Classification: 512.46 .

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Polynomial Identity Rings

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