Solution of the word problem for semigroups without cycles

TL;DR

This paper proves that in semigroups without cycles, the divisibility and word problems are solvable, providing a significant theoretical advancement in understanding these algebraic structures.

Contribution

It establishes the solvability of the word problem in semigroups without cycles, a previously unresolved question in algebra.

Findings

Divisibility problem is solvable in semigroups without cycles

Word problem is solvable in these semigroups

Provides a theoretical foundation for further algebraic research

Abstract

We prove that in an arbitrary semigroup without cycles, the problem of divisibility and, therefore, the word problem is solvable.