TY - JOUR
AU - Ayache, Ahmed
PY - 2019/09/25
Y2 - 2020/04/03
TI - Maximal non-decreasing subring of its quotient field
JF - Gulf Journal of Mathematics
JA - GJOM
VL - 7
IS - 3
SE - Articles
DO -
UR - https://gjom.org/index.php/gjom/article/view/3
SP -
AB - 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.
ER -