The separator of a subset of a semigroup
Attila Nagy
TL;DR
This paper introduces the concept of a separator of a subset in a semigroup using idealizers, explores its properties, and characterizes certain substructures like unitary subsemigroups and prime ideals, including in free semigroups.
Contribution
It defines and studies the separator of a subset in semigroups, providing new characterizations and insights into their structure, especially in free semigroups.
Findings
Characterization of unitary subsemigroups via separator
Identification of prime ideals using separator
Analysis of separators in free subsemigroups
Abstract
In this paper we introduce a new notion by the help of the idealizer. This new notion is the separator of a subset of a semigroup. We investigate the properties of the separator in an arbitrary semigroup and characterize the unitary subsemigroups and the prime ideals by the help of their separator. The last section of this paper treats the separator of a free subsemigroup of a free semigroup.
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Taxonomy
Topicssemigroups and automata theory · Fuzzy and Soft Set Theory · Advanced Algebra and Logic