Network right * abundant semigroups

TL;DR

This paper introduces a new class of semigroups called network right *-abundant semigroups, extending graph inverse semigroups by using network structures, and explores their structural properties and isomorphism conditions.

Contribution

It defines the class of network right *-abundant semigroups and characterizes their isomorphisms based on underlying network isomorphisms.

Findings

Network right *-abundant semigroups extend graph inverse semigroups.

Isomorphism of these semigroups corresponds to network isomorphism.

The class properly contains graph inverse semigroups.

Abstract

We introduce the class of network right $*$-abundant semigroups. These are based on networks that extend the notion of a directed graph. This class properly contains the class of graph inverse semigroups. We investigate the structure of network right $*$-abundant semigroups. We show that two network right $*$-abundant semigroups are isomorphic if and only if the underlying networks are isomorphic.