On finitely presented algebras

TL;DR

This paper proves that under certain conditions involving finitely presented algebras and idempotents, the subalgebra formed by the idempotent is also finitely presented, revealing structural properties of such algebras.

Contribution

It establishes a new result linking the finite presentation of an algebra to that of its subalgebra defined by an idempotent element.

Findings

If $A$ is finitely presented with an idempotent $e$ such that $A=AeA=A(1-e)A$, then $eAe$ is finitely presented.

The result provides insight into the structure of finitely presented algebras and their subalgebras.

The proof relies on properties of idempotents and algebraic presentations.

Abstract

We prove that if $A$ is finitely presented algebra with idempotent $e$ such that $A=AeA=A(1-e)A$ then the algebra $eAe$ is finitely presented.