Maximal non-decreasing subring of its quotient field

  • Ahmed Ayache
Keywords: Going down domain, treed domain, pseudo-valuation domain, valuation domain, minimal overring

Abstract

An integral domain R is called maximal non-going down subring of its quotient field, if R is not going down, and every proper overring of R is going down. We do prove that R is a maximal non-going down subring of its quotient field if and only if R  is a quasi-local domain with maximal ideal m and its integral closure R is a semi-local Prufer domain with two maximal ideals M, N such that M intersect N = m, the extension R is not going down, and R is the unique quasi-local subring of R.

Published
2019-09-25
How to Cite
Ayache, A. (2019). Maximal non-decreasing subring of its quotient field. Gulf Journal of Mathematics, 7(3). Retrieved from https://gjom.org/index.php/gjom/article/view/3
Section
Articles