Geodesic
The Clifford semiring congruences on an additive regular semiring
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 2, pp. 143-153

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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.
Keywords: additive regular semiring, skew-ring, trace, kernel, Clifford congruence 
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Bhuniya, A. The Clifford semiring congruences on an additive regular semiring. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 2, pp. 143-153. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_2_a0/