Open AccessActions of finite groups on commutative rings I
Author(s) -
Adil G. Naoum,
Wassan K.H. Al-Aubaidy
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.34.2003.311
Subject(s) - subring , mathematics , automorphism , commutative property , commutative ring , ideal (ethics) , flatness (cosmology) , property (philosophy) , pure mathematics , multiplication (music) , ring (chemistry) , finite group , discrete mathematics , group ring , group (periodic table) , combinatorics , law , philosophy , chemistry , physics , organic chemistry , cosmology , epistemology , quantum mechanics , political science
Let $R$ be a commutative ring with 1, and let $G$ be a finite group of automorphisms of $R$. Denote by $R^G$ the fixed subring of $G$, and let $I$ be a subset of $R^G$. In this paper we prove that if the ideal generated by $I$ in $R$ satisfies a certain property with regard to projectivity, flatness, multiplication or related concepts, then the ideal generated by $I$ in $R^G$ also satisfies the same property