Categories and General Algebraic Structures with Applications

Categories and General Algebraic Structures with Applications

Commutative subdirectly irreducible semigroups

Articles in Press

Document Type : Research Paper

Author
Mojtaba Sedaghatjoo
Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, 751-6913817, Iran
10.48308/cgasa.2026.244895.1636
Abstract
This paper aims to establish a structural characterization of subdirectly irreducible commutative semigroups. We unify the three classes of semigroups introduced by Schein into a single structure. Furthermore, we characterize the distinction between irreducible and subdirectly irreducible commutative semigroups.
Keywords
Commutative semigroups
subdirectly irreducible
irreducible
weakly essential
disjunctive
Subjects
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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 18 September 2026