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Two generalizations of T-nilpotence

Citation

Gardner, BJ and Kelarev, AV, Two generalizations of T-nilpotence, Algebra Colloquium, 5, (4) pp. 449-458. ISSN 1005-3867 (1998) [Refereed Article]

Abstract

A commutative ring R is called T-idempotent if, for every sequence r1,r2,⋯ ∈ R, there exists a positive integer n and an idempotent e ∈ R such that r1 ⋯rn = e. A commutative ring R is called T-stable if, for every sequence r1,r2,⋯ R, there exists a positive integer n such that r1⋯rn = r1⋯rn+1 = ⋯. We show that a commutative ring is T-idempotent if and only if it is the direct product of a T-nilpotent ring and a Boolean ring. We prove that a commutative ring is T-stable if and only if it is the direct product of a T-nilpotent ring and a Boolean ring satisfying the descending chain condition for idempotents. We describe all commutative T-idempotent and T-stable semigroup rings. © Springer-Verlag 1998.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Algebra and Number Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Gardner, BJ (Dr Barry Gardner)
Author:Kelarev, AV (Dr Andrei Kelarev)
ID Code:14018
Year Published:1998
Web of Science® Times Cited:1
Deposited By:Mathematics
Deposited On:1998-08-01
Last Modified:2011-08-09
Downloads:0

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