A construction of a finitely presented semigroup containing nonnilpotent nil ideal

TL;DR

This paper constructs a finitely presented semigroup with a nonnilpotent nil ideal where elements lack squares, illustrating complex algebraic structures and properties within semigroup theory.

Contribution

It provides a novel example of a finitely presented semigroup with a nonnilpotent nil ideal exhibiting unique element properties.

Findings

Existence of a finitely presented semigroup with a nonnilpotent nil ideal

Elements in the ideal do not have squares, i.e., certain words equal zero

The semigroup demonstrates complex algebraic behavior

Abstract

This work presents an example of a finitely presented semigroup $S$ containing an infinite nonnilpotent nil ideal $LS$, whose elements do not have a square (i.e. any word of the type $LXYYZ$ equals zero.)