On semidualizing modules of ladder determinantal rings

TL;DR

This paper classifies all semidualizing modules over specific ladder determinantal rings, showing that only trivial modules exist in certain cases, thus advancing understanding of their module structure.

Contribution

It identifies conditions under which ladder determinantal rings have only trivial semidualizing modules, expanding knowledge of their algebraic properties.

Findings

Only trivial semidualizing modules in one-sided ladders.

Only trivial semidualizing modules in two-sided ladders with t=2 and no coincidental inside corners.

Provides a complete classification for these classes of rings.

Abstract

We identify all semidualizing modules over certain classes of ladder determinantal rings over a field ${\mathsf k}$. Specifically, given a ladder of variables $Y$, we show that the ring ${\mathsf k}[Y]/I_t(Y)$ has only trivial semidualizing modules up to isomorphism in the following cases: (1) $Y$ is a one-sided ladder, and (2) $Y$ is a two-sided ladder with $t=2$ and no coincidental inside corners.