WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Some Study on the Topological Structure on Semigroups
Authors: , ,
Abstract: Some studies related to the topological structure of semigroups are provided. In, [3], considering
and investigating the properties of the collection A of all the proper uniformly strongly prime ideals of a Γ - semigroup S, such study starts by constructing a topology $$τ_{A} $$ on A using a closure operator defined in terms of the intersection and inclusion relation among these ideals of Γ-semigroup S, which is a generalization of the
semigroup. In this paper, we introduce three other classes of ideals in semigroups called maximal ideals, prime
ideals and strongly irreducible ideals, respectively. Investigating properties of the collection M, B and S of all
proper maximal ideals, prime ideals and strongly irreducible ideals, respectively, of a semigroup S, we
construct the respective topologies on them. The respective obtained topological spaces are called the structure
spaces of the semigroup S. We study several principal topological axioms and properties in those structure
spaces of semigroup such as separation axioms, compactness and connectedness, etc.
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Keywords: Semigroup, prime ideal, maximal ideal, strongly irreducible ideal, structure space, hull-kernel topology
Pages: 779-784
DOI: 10.37394/23206.2022.21.89