Open AccessAnnihilator-semigroup rings
Author(s) -
D. D. Anderson,
Victor Camillo
Publication year - 2003
Publication title -
tamkang journal of mathematics (online)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.34.2003.313
Subject(s) - annihilator , mathematics , semigroup , ring (chemistry) , multiplicative function , pure mathematics , commutative ring , commutative property , discrete mathematics , ideal (ethics) , algebra over a field , mathematical analysis , law , chemistry , organic chemistry , political science
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