Pairs of rings invariant under group action

  • Nabil ZeidiEmail author
Original Paper


Let \(R\subseteq S\) be a ring extension and \(\mathcal {P}\) be a ring-theoretic property. The pair (RS) is said to be a \(\mathcal {P}\)-pair if, T satisfies \(\mathcal {P}\) for each intermediate ring \(R\subseteq T\subseteq S\). Let G be a subgroup of the automorphism group of S such that R is invariant under the action by G. In this paper we investigate in several cases the transfer of a property \(\mathcal {P}\) from the pair (RS) to \((R^G,S^G)\). For instance, if \(\mathcal {P}:=\) Residaully algebraic, LO, INC, and Valuation, we show that each of these properties pass from (RS) to \((R^G,S^G)\). Additional consequences and applications are given.


Normal pair Valuation domain LO & INC Treed domain Ring of invariants Group action 

Mathematics Subject Classification

Primary 13B02 13A50 Secondary 13A15 13A18 13B22 



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Copyright information

© The Managing Editors 2020

Authors and Affiliations

  1. 1.Faculty of Sciences, Department of MathematicsSfax UniversitySfaxTunisia

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