arXiv subjects
Publications and source records attributed to Anam Rani.
We extend to rings with zero-divisors the concept of perinormal domain introduced by N. Epstein and J. Shapiro. A ring $A$ is called perinormal if every overring of $A$ which satisfies going down over $A$ is $A$-flat. The Prüfer rings and the Marot Krull rings are perinormal.
Recently, N. Epstein and J. Shapiro introduced and studied the perinormal domains: those domains A whose going down overrings are flat A-modules. We show that every Prüfer v-multiplication domain is perinormal and has no proper lying over overrings. We also show that a treed perinormal domain is a Prüfer domain. We give two pull-back constructions that produce perinormal/non-perinormal domains.