International Journal of Mathematics Trends and Technology
Volume 70 | Issue 9 | Year 2024 | Article Id. IJMTT-V70I9P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I9P102
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 24 Jul 2024 | 27 Aug 2024 | 14 Sep 2024 | 30 Sep 2024 |
In this study, the basic characteristics of semigroups, a basic idea in algebraic structures, are examined, along with
their several classifications. A single associative binary operation defines semigroups, which have a variety of characteristics
that affect how they behave structurally. The fundamental characteristics that set semigroups apart from other algebraic
structures like groups and monoids such as associativity, identity elements, and idempotency—are thoroughly examined at the
outset of this research. The classification of semigroups according to particular characteristics like commutativity, regularity,
and simplicity is further examined in this study. The significance of Green’s relations for categorizing semigroups and
comprehending their internal organization is highlighted in particular. The research also looks at the applications of these
categories in automata theory, coding theory, and dynamic system modelling, among other more general mathematical
contexts. This study attempts to give a clearer knowledge of the fundamental nature of semigroups and their role within
algebra through an extensive survey of the existing literature and the introduction of new viewpoints on semigroup properties.
The results provide information that could stimulate additional investigation into semigroups and applications in a variety of
mathematical fields.
Semigroups, Algebraic structures, Regular semigroups, Inverse semigroups, Green’s relations.
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Nikuanj Kumar, Bijendra Kumar, "Some Fundamental Properties of Semigroups and their Classifications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 9, pp. 8-11, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I9P102
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