On ∼n Notion of Conjugacy in Some Classes of Epigroups
The action of any group on itself by conjugation and the corresponding conjugacy relation plays an important role in group theory. Generalizing the group theoretic notion of conjugacy to semigroups is one of the interesting problems, and semigroup theorists had produced substantial amount of researc...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/8414022 |
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| author | Aftab Hussain Shah Amal S. Alali Mohd Rafiq Parray |
| author_facet | Aftab Hussain Shah Amal S. Alali Mohd Rafiq Parray |
| author_sort | Aftab Hussain Shah |
| collection | DOAJ |
| description | The action of any group on itself by conjugation and the corresponding conjugacy relation plays an important role in group theory. Generalizing the group theoretic notion of conjugacy to semigroups is one of the interesting problems, and semigroup theorists had produced substantial amount of research in this direction. The challenge to introduce a new notion of conjugacy in semigroups is to choose the suitable set of conjugating elements. A semigroup may contain a zero, and if zero lies in the conjugating set, then the relation reduces to the universal relation as can be seen in the notions ∼l, ∼p, and ∼o. To avoid this problem, various innovative notions of conjugacy in semigroups have been considered so far, and ∼n is one of these notions. ∼n is an equivalence relation in any semigroup, coincides with the usual group theoretic notion if the underlying semigroup is a group, and does not reduce to a universal relation even if S contains a zero. In this paper, we study ∼n notion of conjugacy in some classes of epigroups. Since epigroups are generalizations of groups, our results of this paper are innovative and generalize the existing results on other notions. After proving some fundamental results, we compare our results with existing ones and prove that they are worth contribution in the study of conjugacy in epigroups. |
| format | Article |
| id | doaj-art-e53d0132824c4fea958049f57224e684 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e53d0132824c4fea958049f57224e6842025-02-03T01:30:22ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/8414022On ∼n Notion of Conjugacy in Some Classes of EpigroupsAftab Hussain Shah0Amal S. Alali1Mohd Rafiq Parray2Department of MathematicsDepartment of Mathematical SciencesDepartment of MathematicsThe action of any group on itself by conjugation and the corresponding conjugacy relation plays an important role in group theory. Generalizing the group theoretic notion of conjugacy to semigroups is one of the interesting problems, and semigroup theorists had produced substantial amount of research in this direction. The challenge to introduce a new notion of conjugacy in semigroups is to choose the suitable set of conjugating elements. A semigroup may contain a zero, and if zero lies in the conjugating set, then the relation reduces to the universal relation as can be seen in the notions ∼l, ∼p, and ∼o. To avoid this problem, various innovative notions of conjugacy in semigroups have been considered so far, and ∼n is one of these notions. ∼n is an equivalence relation in any semigroup, coincides with the usual group theoretic notion if the underlying semigroup is a group, and does not reduce to a universal relation even if S contains a zero. In this paper, we study ∼n notion of conjugacy in some classes of epigroups. Since epigroups are generalizations of groups, our results of this paper are innovative and generalize the existing results on other notions. After proving some fundamental results, we compare our results with existing ones and prove that they are worth contribution in the study of conjugacy in epigroups.http://dx.doi.org/10.1155/2024/8414022 |
| spellingShingle | Aftab Hussain Shah Amal S. Alali Mohd Rafiq Parray On ∼n Notion of Conjugacy in Some Classes of Epigroups Journal of Mathematics |
| title | On ∼n Notion of Conjugacy in Some Classes of Epigroups |
| title_full | On ∼n Notion of Conjugacy in Some Classes of Epigroups |
| title_fullStr | On ∼n Notion of Conjugacy in Some Classes of Epigroups |
| title_full_unstemmed | On ∼n Notion of Conjugacy in Some Classes of Epigroups |
| title_short | On ∼n Notion of Conjugacy in Some Classes of Epigroups |
| title_sort | on ∼n notion of conjugacy in some classes of epigroups |
| url | http://dx.doi.org/10.1155/2024/8414022 |
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