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Displaying similar documents to “Semirings embedded in a completely regular semiring”

A note on orthodox additive inverse semirings

M. K. Sen, S. K. Maity (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We show in an additive inverse regular semiring ( S , + , · ) with E ( S ) as the set of all multiplicative idempotents and E + ( S ) as the set of all additive idempotents, the following conditions are equivalent: (i) For all e , f E ( S ) , e f E + ( S ) implies f e E + ( S ) . (ii) ( S , · ) is orthodox. (iii) ( S , · ) is a semilattice of groups. This result generalizes the corresponding result of regular ring.

The Clifford semiring congruences on an additive regular semiring

A.K. Bhuniya (2014)

Discussiones Mathematicae - General Algebra and Applications

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A congruence ρ on a semiring S is called a (generalized)Clifford semiring congruence if S/ρ is a (generalized)Clifford semiring. Here we characterize the (generalized)Clifford congruences on a semiring whose additive reduct is a regular semigroup. Also we give an explicit description for the least (generalized)Clifford congruence on such semirings.