Annihilator-semigroup rings

descriptionPublicationkeyboard_double_arrow_right Article 30 Sep 2003Publisher:Tamkang Journal of MathematicsJournal:Tamkang Journal of Mathematics, volume 34, pages 223-229 (issn: 0049-2930, eissn: 2073-9826,

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Authors: Anderson, D. D.; Camillo, Victor;

doi: 10.5556/j.tkjm.34.2003.313

Annihilator-semigroup rings

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Abstract

Let $ R $ be a commutative ring with 1. We define $ R $ to be an annihilator-semigroup ring if $ R $ has an annihilator-Semigroup $ S $, that is, $ (S, \cdot) $ is a multiplicative subsemigroup of $ (R, \cdot) $ with the property that for each $ r \in R $ there exists a unique $ s \in S $ with $ 0 : r = 0 : s $. In this paper we investigate annihilator-semigroups and annihilator-semigroup rings.

Keywords

General commutative ring theory, Ordinary and skew polynomial rings and semigroup rings, annihilator-semigroup ring, P.P. ring

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