Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorDrensky, Vesselin. author
TitlePolynomial Identity Rings [electronic resource] / by Vesselin Drensky, Edward Formanek
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004
Connect tohttp://dx.doi.org/10.1007/978-3-0348-7934-7
Descript VII, 200 p. online resource

SUMMARY

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


CONTENT

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 Kaplanskyโ{128}{153}s Theorem -- 5 Theorems of Amitsur and Levitzki on Radicals -- 6 Posnerโ{128}{153}s Theorem -- 7 Every PI-ring Satisfies a Power of the Standard Identity -- 8 Azumaya Algebras -- 9 Artinโ{128}{153}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?


Mathematics Associative rings Rings (Algebra) Combinatorics Mathematics Associative Rings and Algebras Combinatorics



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram