Von Neumann regularity of smash products associated with G-set gradings

Leonard Daua*, Constantin Nastasescu, Maria Monica Nastasescu

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

For a G-graded ring R, the problem of Gr-regularity (i.e. von Neumann regularity condition on homogeneous elements) has been treated earlier (see Nǎstǎsescu and Van Oystaeyen, 1982 [11]). Once the concept of the smash product was introduced, this problem has been resumed by several authors. This paper is concerned with von Neumann regularity of two smash products: the smash product R#G of the G-graded ring R by the group G and the smash product R#A of R by a finite left G-set A. The connections between the regularity of R#A and the (Gr-)regularity of R are also investigated. One consequence of our results is that the smash product R#A is a von Neumann regular ring if and only if the category (G,A,R)- gr is regular, in Stenström's sense.

Original languageEnglish (US)
Pages (from-to)46-57
Number of pages12
JournalJournal of Algebra
Volume331
Issue number1
DOIs
StatePublished - Apr 1 2011

Keywords

  • Graded ring
  • Smash product
  • Von Neumann regular ring

ASJC Scopus subject areas

  • Algebra and Number Theory

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