Actions of finite groups on commutative rings I | Zendy

Adil G. Naoum | Zendy; Wassan K.H. Al-Aubaidy | Zendy

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Actions 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

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

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