On Residually (Completely) Integrally Closed Rings
Ali Tamoussit
Department of Mathematics, The Regional Center for Education and Training Professions Souss
Massa, Inezgane, Morocco.
Pages 187-196 | Received 09 November 2023, Accepted 11 January 2024, Published 30 June 2024
Abstract
All rings considered in this paper are commutative rings with identity. A ring R is called a residually completely
integrally closed (for short, RCIC) ring if the integral domain R/P is completely integrally closed, for all prime ideals P of R. The main goal of this paper is to study the behavior of the RCIC property in some distinguished constructions such as homomorphic image, finite direct products, Nagata ring, amalgamated duplications of rings and trivial ring extensions. Our study is then extended to the case of residually integrally closed rings.
Keywords: (Completely) integrally closed, Nagata ring, amalgamated duplication, trivial ring extension.
MSC numbers: Primary 13A15, 13B22; Secondary 13B02, 13F99.
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