Finite homotopy bases of one-relator monoids (Q1579154)

The author continues his studies of homotopy bases of monoids [J. Pure Appl. Algebra 130, No. 2, 159-195 (1998; Zbl 0932.20053)]. A monoid \(M\) which has a presentation of type \((\Sigma,e)\), \(e\in\Sigma^*\times\Sigma^*\), is said to be a one-relator monoid. A parallel relation \(\parallel\) on the derivation graph of \(M\) is defined in a natural way consisting of all pairs \((p,q)\) with the same source and the same target. Any equivalence relation contained in \(\parallel\) and satisfying certain conditions is called a homotopy relation and any generating subset of \(\parallel\) is called a homotopy base. The main theorem states that every one-relator monoid has a finite homotopy base.