Identities of graded simple algebras

Dušan Repovš (Author), Mikhail Zaicev (Author)

Abstract

We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid ▫$\Gamma$▫. First, we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra ▫$A$▫, we prove the existence of the graded PI-exponent, provided that ▫$\Gamma$▫ is a commutative semigroup. If ▫$A$▫ is simple in a non-graded sense, the existence of the graded PI-exponent is proved without any restrictions on ▫$\Gamma$▫.

Keywords

polynomial identities;graded algebras;codimensions;exponential growth;

Data

Language:	English
Year of publishing:	2017
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	512.554
COBISS:	17652313
ISSN:	0308-1087
Views:	516
Downloads:	316
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 44-57
Volume:	ǂVol. ǂ65
Issue:	ǂiss. ǂ1
Chronology:	2017
DOI:	10.1080/03081087.2016.1167160
ID:	11222874