On semirings whose additive reduct is a semilattice |
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Authors: | M K Sen A K Bhuniya |
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Affiliation: | 1.Department of Pure Mathematics,University of Calcutta,Kolkata,India;2.Department of Mathematics,Visva-Bharati,Santiniketan,India |
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Abstract: | A semiring S whose additive reduct is a semilattice is called a k-regular semiring if for every a∈S there is x∈S such that a+axa=axa. For a semigroup F, the power semiring P(F) is a k-regular semiring if and only if F is a regular semigroup. An element e∈S is a k-idempotent if e+e
2=e
2. Basic properties of k-regular semirings whose k-idempotents are commutative have been studied. |
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Keywords: | |
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