The Journal of the Indian Mathematical Society

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Additively and Multiplicatively Inverse Near-Semirings


Affiliations
1 Department of Mathematics, Annamalai University, Annamalainagar - 608 002, India
     

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It has been shown that in a near-semiring (S,+,.) with (S,+) as an inverse semigroup, the near-semiring S is strongly regular if and only if S is regular and reduced. In a near-semiring (S,+,.) with (S,+) as an inverse semigroup, equivalent conditions are obtained such that (S,.) is also an inverse semigroup.

Keywords

Inverse Semigroup, Reduced, Regular, Strongly Regular.
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  • Additively and Multiplicatively Inverse Near-Semirings

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Authors

P. Dheena
Department of Mathematics, Annamalai University, Annamalainagar - 608 002, India
C. Jenila
Department of Mathematics, Annamalai University, Annamalainagar - 608 002, India

Abstract


It has been shown that in a near-semiring (S,+,.) with (S,+) as an inverse semigroup, the near-semiring S is strongly regular if and only if S is regular and reduced. In a near-semiring (S,+,.) with (S,+) as an inverse semigroup, equivalent conditions are obtained such that (S,.) is also an inverse semigroup.

Keywords


Inverse Semigroup, Reduced, Regular, Strongly Regular.