Chain conditions on convolution rings

Stefan Veldsman

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The notion of a convolution type has been introduced earlier. Imposing such a type on a ring gives the corresponding convolution ring. Under this umbrella, a wide variety of ring constructions can be covered, including polynomials, matrices, incidence algebras, necklace rings, group rings, and quaternion rings. Here conditions on the parameters of the convolution type to ensure that the corresponding convolution rings enjoy certain algebraic properties will be investigated. In particular, the requirements for the convolution rings to satisfy chain conditions are determined.

Original languageEnglish
Pages (from-to)371-388
Number of pages18
JournalCommunications in Algebra
Volume35
Issue number1
DOIs
Publication statusPublished - Jan 2007

Fingerprint

Chain Condition
Convolution
Ring
Incidence Algebra
Necklace
Polynomial Matrices
Group Ring
Quaternion
Requirements

Keywords

  • Artinian
  • Convolution rings
  • Incidence algebra
  • Matrix rings
  • Necklace ring
  • Noetherian
  • Polynomial rings

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Chain conditions on convolution rings. / Veldsman, Stefan.

In: Communications in Algebra, Vol. 35, No. 1, 01.2007, p. 371-388.

Research output: Contribution to journalArticle

Veldsman, Stefan. / Chain conditions on convolution rings. In: Communications in Algebra. 2007 ; Vol. 35, No. 1. pp. 371-388.
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