Identities of graded simple algebras

Repovš, Dušan (author), Zaicev, Mikhail V. (author)

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 ▫$\Gamma$▫.

• Language: English
• Keywords: polynomial identities, graded algebras, codimensions, exponential growth
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2017
• Number of pages: Str. 44-57
• Numbering: Vol. 65, iss. 1
• PID: 20.500.12556/RUL-110327
• UDC: 512.554
• ISSN on article: 0308-1087
• DOI: 10.1080/03081087.2016.1167160
• COBISS.SI-ID: 17652313
• Publication date in RUL: 13.09.2019

Record is a part of a journal

• Title: Linear and multilinear algebra
• Shortened title: Linear multilinear algebra
• Publisher: Taylor & Francis
• ISSN: 0308-1087
• COBISS.SI-ID: 25872128