2007•Journal of Algebra and Its ApplicationsRequires access

MAXIMAL NON-UNIVERSALLY CATENARIAN SUBRINGS OF A FIELD: THE NON-INTEGRALLY CLOSED CASE

Mabrouk Ben Nasr

Abstract

In this paper, we deal with the study of maximal non-universally catenarian subrings (that is a non-universally catenarian subring R of a domain S such that any subring of S that properly contains R is universally catenarian). Several satisfactory results are given, and for S a field and R not integrally closed, we characterize these domains.

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Key concepts: Integrally closed, Subring, Mathematics, Pure mathematics, Field (mathematics), Domain (mathematical analysis), Discrete mathematics, Ring (chemistry)