The zero-level centralizer in endomorphism algebras

TL;DR

This paper studies the structure and identities of the zero-level centralizer in endomorphism algebras, revealing new algebraic properties and a double centralizer theorem.

Contribution

It introduces a detailed analysis of the zero-level centralizer and establishes a double zero-centralizer theorem for endomorphism algebras.

Findings

Characterization of the structure of Cen_0(f)

Identification of polynomial identities of Cen_0(f) and its factor

A double zero-centralizer theorem for Cen_0(Cen_0(f))

Abstract

For an endomorphism f\inEnd{M) of a left R-module M we investigate the structure and the polynomial identities of the zero-level centralizer Cen_0(f) and the factor Cen(f)/Cen_0(f). A double zero-centralizer theorem for Cen_0(Cen_0(f)) is also formulated.