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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |