Square-Free Rings With Local Units

TL;DR

This paper extends the characterization of artinian square-free rings with identity to rings with local units, providing new results and cohomological conditions for their algebraic structures.

Contribution

It generalizes previous results on square-free rings to include rings with local units and explores their algebraic and cohomological properties.

Findings

Extended characterization to rings with local units

Derived conditions for square-free rings to have algebra structures

Provided cohomological criteria for algebraic structures

Abstract

Recently, the author characterized all artinian square-free rings with identity. Here, those results are extended to the setting of rings with local units. We use this characterization of square-free rings to derive many results similar to the artinian case and to determine, in cohomological terms, exactly when a square-free ring has an associated square-free algebra structure.