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- Title
Δ-Extension of rings and invariance properties of ring extension under group action.
- Authors
Kumar, Rahul; Gaur, Atul
- Abstract
Let R , T be commutative rings with identity such that R ⊆ T. A ring extension R ⊆ T is called a Δ -extension of rings if R 1 + R 2 is a subring of T for each pair of subrings R 1 , R 2 of T containing R. In this paper, a characterization of integrally closed Δ -extension of rings is given. The equivalence of Δ -extension of rings and λ -extension of rings is established for an integrally closed extension of a local ring. Over a finite dimensional, integrally closed extension of local rings, the equivalence of Δ -extensions of rings, FIP, and FCP is shown. Let R be a subring of T such that R is invariant under action by G , where G is a subgroup of the automorphism group of T. If R ⊆ T is a Δ -extension of rings, then R G ⊆ T G is a Δ -extension of rings under some conditions. Many such G -invariant properties are also discussed.
- Subjects
RING extensions (Algebra); MATHEMATICAL symmetry; GROUP actions (Mathematics); COMMUTATIVE rings; INTEGRALS; AUTOMORPHISM groups
- Publication
Journal of Algebra & Its Applications, 2018, Vol 17, Issue 12, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498818502390