Ladder determinantal rings over normal domains

TL;DR

This paper provides explicit descriptions of divisor class groups and semidualizing modules for ladder determinantal rings over arbitrary normal domains, covering all ladder configurations and minors.

Contribution

It extends the understanding of ladder determinantal rings by generalizing to arbitrary ladders and coefficients in any normal domain, including disconnected cases.

Findings

Explicit formulas for divisor class groups.

Characterization of semidualizing modules.

Applicability to all ladder sizes and configurations.

Abstract

We explicitly describe the divisor class groups and semidualizing modules for ladder determinantal rings with coefficients in an arbitrary normal domain for arbitrary ladders, not necessarily connected, and all sizes of minors.