The Source of Semiprimeness of Semigroups
In this study, we define new semigroup structures using the set SS=a∈S|aSa=0 which is called the source of semiprimeness for a semigroup S with zero element. SS−idempotent semigroup, SS−regular semigroup, SS−reduced semigroup, and SS−nonzero divisor semigroup which are generalizations of idempotent,...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4659756 |
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| _version_ | 1832546039074127872 |
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| author | Barış Albayrak Didem Yeşil Didem Karalarlioğlu Camci |
| author_facet | Barış Albayrak Didem Yeşil Didem Karalarlioğlu Camci |
| author_sort | Barış Albayrak |
| collection | DOAJ |
| description | In this study, we define new semigroup structures using the set SS=a∈S|aSa=0 which is called the source of semiprimeness for a semigroup S with zero element. SS−idempotent semigroup, SS−regular semigroup, SS−reduced semigroup, and SS−nonzero divisor semigroup which are generalizations of idempotent, regular, reduced, and nonzero divisor semigroups in semigroup theory are investigated, and their basic properties are determined. In addition, we adapt some well-known results in semigroup theory to these new semigroups. |
| format | Article |
| id | doaj-art-11cbe66fa0db4a3abd67fa34a0526096 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-11cbe66fa0db4a3abd67fa34a05260962025-02-03T07:24:00ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/46597564659756The Source of Semiprimeness of SemigroupsBarış Albayrak0Didem Yeşil1Didem Karalarlioğlu Camci2Çanakkale Onsekiz Mart University, Biga Faculty of Applied Sciences, Department of Banking and Finance, Çanakkale, TurkeyÇanakkale Onsekiz Mart University, Faculty of Arts and Sciences, Department of Mathematics, Çanakkale, TurkeyÇanakkale Onsekiz Mart University, Faculty of Arts and Sciences, Department of Mathematics, Çanakkale, TurkeyIn this study, we define new semigroup structures using the set SS=a∈S|aSa=0 which is called the source of semiprimeness for a semigroup S with zero element. SS−idempotent semigroup, SS−regular semigroup, SS−reduced semigroup, and SS−nonzero divisor semigroup which are generalizations of idempotent, regular, reduced, and nonzero divisor semigroups in semigroup theory are investigated, and their basic properties are determined. In addition, we adapt some well-known results in semigroup theory to these new semigroups.http://dx.doi.org/10.1155/2021/4659756 |
| spellingShingle | Barış Albayrak Didem Yeşil Didem Karalarlioğlu Camci The Source of Semiprimeness of Semigroups Journal of Mathematics |
| title | The Source of Semiprimeness of Semigroups |
| title_full | The Source of Semiprimeness of Semigroups |
| title_fullStr | The Source of Semiprimeness of Semigroups |
| title_full_unstemmed | The Source of Semiprimeness of Semigroups |
| title_short | The Source of Semiprimeness of Semigroups |
| title_sort | source of semiprimeness of semigroups |
| url | http://dx.doi.org/10.1155/2021/4659756 |
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