Rings with polynomial identity and centrally essential rings

Abstract

It is proved that for any prime integer p and each field F of characteristic p, there exists a centrally essential F -algebra which is not a PI-ring and is not algebraic over its center.V.T.Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. A.A.Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.Key words: centrally essential ring, PI ring, ring algebraic over its center, ring integral over its center. MSC2010 datebase 16R99; 16D101 Centrally essential rings are studied, for example, in [1].

Centrally Essential Rings and Semirings

“…The main results of this subsection are proved in [12]. Let X be a countable set and let F = Z X be the free ring with free generator set X.…”

“…In this case, all matrices in A c are contained in Cen(A). Then A c consists of matrices of the form (12) and matrices in Z(A c ) of the form (13). However, AC = 0 for any matrix C ∈ Z(A c ).…”

“…The work is based on papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The author is very grateful for the great help in editing the manuscript to Adel Abyzov, Oleg Lyubimtsev and Danil Tapkin.…”