On special Rees matrix semigroups over semigroups
Attila Nagy, Csaba T\'oth

TL;DR
This paper investigates special Rees matrix semigroups over semigroups, describing their kernels, embedding properties, and constructing right commutative right cancellative semigroups, with a focus on algebraic structure and congruences.
Contribution
It introduces a detailed analysis of Rees matrix semigroups with specific sandwich matrices and establishes new embedding theorems and constructions for related semigroups.
Findings
Kernel of the right regular representation characterized
Embedding theorems for these semigroups proved
Construction method for right commutative right cancellative semigroups
Abstract
In this paper we focus on Rees matrix semigroups without zero over a semigroup with sandwich matrix , where is a singleton, is the factor semigroup of modulo the kernel of the right regular representation of , and is a choice function on the collection of all -classes of . We describe the kernel of the right regular representation of this type of Rees matrix semigroups, and prove embedding theorems on them. Motivated by one of embedding theorems, we show how right commutative right cancellative semigroups can be constructed. We define the concept of a right regular sequence of semigroups, and show that every congruence on an arbitrary semigroup defines such a sequence.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Fuzzy and Soft Set Theory
