Totally compatible structures on the radical of an incidence algebra

TL;DR

This paper characterizes totally compatible algebraic structures on the radical of incidence algebras of finite posets, revealing that these structures are generally non-proper.

Contribution

It provides a description of totally compatible structures on the Jacobson radical of incidence algebras, highlighting their typical non-proper nature.

Findings

Totally compatible structures on the radical are generally non-proper.

The paper offers a characterization of these structures for finite posets.

It advances understanding of algebraic structures on incidence algebra radicals.

Abstract

We describe totally compatible structures on the Jacobson radical of the incidence algebra of a finite poset over a field. We show that such structures are in general non-proper.