A characterization of minimal varieties of Zp-graded PI algebras

被引：15

作者：

Di Vincenzo, Onofrio Mario ^{[1
]}

Tomaz da Silva, Viviane Ribeiro ^{[2
]}

Spinelli, Ernesto ^{[3
]}

机构：

[1] Univ Basilicata, Dipartimento Matemat Informat Econ, Via Ateneo Lucano 10, I-85100 Potenza, Italy

[2] Univ Fed Minas Gerais, Inst Ciencias Exatas, Dept Matemat, BR-30161970 Belo Horizonte, MG, Brazil

[3] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

来源：

JOURNAL OF ALGEBRA | 2019年 / 539卷

关键词：

Graded algebras; Graded polynomial identities; G-exponent; Minimal varieties; Upper block triangular matrix algebras; GRADED POLYNOMIAL-IDENTITIES; CODIMENSION GROWTH; SUPERVARIETIES; EXISTENCE;

D O I：

10.1016/j.jalgebra.2019.08.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F be a field of characteristic zero and p a prime. In the present paper it is proved that a variety of Z(p)-graded associative PI F-algebras of finite basic rank is minimal of fixed Z(p)-exponent d if, and only if, it is generated by an upper block triangular matrix algebra UTz(p) (A(1), ..., A(m)) equipped with a suitable elementary Z(p)-grading, whose diagonal blocks are isomorphic to Z(p)-graded simple algebras A(1), ..., A(m) satisfying dim(F)(A(1) circle plus ... circle plus A(m)) = d. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：397 / 418

页数：22

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