Basically regular local homomorphisms

TL;DR

This paper studies a specific class of local homomorphisms called basically regular, analyzing their properties, numerical characterizations, and how they relate to other known classes of homomorphisms in commutative algebra.

Contribution

It introduces and characterizes basically regular local homomorphisms, expanding understanding of regularity transfer in local ring theory.

Findings

Numerical criteria for basically regular homomorphisms

Behavior under composition and decomposition analyzed

Comparison with weakly regular homomorphisms conducted

Abstract

We investigate the transfer of regularity between commutative, noetherian, local rings through a class of local homomorphisms which we call basically regular. We give numerical characterizations of these maps, investigate their behavior under composition and decomposition, and compare them with Avramov-Foxby-Herzog's weakly regular local homomorphisms.