Vesselin Drensky

Vesselin Drensky; Edward Formanek

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 Kaplanskys Theorem.- 5 Theorems of Amitsur and Levitzki on Radicals.- 6 Posners Theorem.- 7 Every PI-ring Satisfies a Power of the Standard Identity.- 8 Azumaya Algebras.- 9 Artins 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?.

Yuri Bahturin; Vesselin Drensky

We consider G-graded polynomial identities of the p×p matrix algebra Mp(K) over a field K of characteristic 0 graded by an arbitrary group G. We find relations between the G-graded identities of the G-graded algebra Mp(K) and the (G×H)-graded identities of the tensor product of Mp(K) and the H-graded algebra Mq(K) with a fine H-grading. We also find a basis of the G-graded identities of Mp(K) with an elementary grading such that the identity component coincides with the diagonal of Mp(K).

Vesselin Drensky; Amitai Regev

AbstractLetcn(A) denote the codimensions of a P.I. algebraA, and assumecn(A) has a polynomial growth:

Helmer Aslaksen; Vesselin Drensky; Liliya Sadikova

Vesselin Drensky

c_n (A)_{n_{ \to \infty }^ \simeq } qn^k

Vesselin Drensky

Vesselin Drensky; Georgi K. Genov

. Then, necessarily,q∈ℚ [D3]. If 1∈A, we show that

Vesselin Drensky; Tsetska Rashkova

Vesselin Drensky

\frac{1}{{k!}} \leqslant q \leqslant \frac{1}{{2!}} - \frac{1}{{3!}} + - \cdot \cdot \cdot + \frac{{( - 1)^k }}{{k!}} \approx \frac{1}{e}

Vesselin Drensky; Jie-Tai Yu