w-Stability and Clifford w-Regularity of Polynomial Rings

TL;DR

This paper explores how properties called w-stability and Clifford w-regularity transfer from a base domain to its polynomial ring, focusing on cases where the domain is integrally closed or Mori w-divisorial.

Contribution

It establishes conditions under which w-stability and Clifford w-regularity are preserved in polynomial rings, extending understanding of these properties in algebraic structures.

Findings

w-stability and Clifford w-regularity transfer from D to D[X] when D is integrally closed

Transfer also occurs if D is Mori and w-divisorial

Provides new criteria for property transfer in polynomial extensions

Abstract

We investigate the transfer of w-stability and Clifford w-regularity from a domain D to the polynomial ring D[X]. We show that these two properties pass from D to D[X] when D is either integrally closed or it is Mori and w-divisorial.