Geodesic
The Clifford semiring congruences on an additive regular semiring
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 2, pp. 143-153 Cet article a éte moissonné depuis la source Library of Science

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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/

[1] H.J. Bandelt and M. Petrich, Subdirect products of rings and distributive lattices, Proc. Edin. Math. Soc. 25 (1982) 155-171. doi: 10.1017/S0013091500016643

[2] R. Feigenbaum, Kernels of regular semigroup homomorphisms. Doctoral Dissertation (University of South Carolina, 1975).

[3] R. Feigenbaum, Regular semigroup congruences, Semigroup Forum 17 (1979) 373-377. doi: 10.1007/BF02194336

[4] S. Ghosh, A characterisation of semirings which are subdirect products of a distributive lattice and a ring, Semigroup Forum 59 (1999) 106-120. doi: 10.1007/PL00005999

[5] J.S. Golan, Semirings and Their Applications (Kluwer Academic Publishers, Dordrecht, 1999).

[6] M.P. Grillet, Semirings with a completely simple additive Semigroup, J. Austral. Math. Soc. 20 (A) (1975) 257-267. doi: 10.1017/S1446788700020607

[7] J.M. Howie, Fundamentals of semigroup theory (Clarendon, Oxford, 1995). Reprint in 2003.

[8] D.R. LaTorre, The least semilattice of groups congruence on a regular semigroup, Semigroup Forum 27 (1983) 319-329. doi: 10.1007/BF02572745

[9] S.K. Maity, Congruences on additive inverse semirings, Southeast Asian Bull. Math. 30 (3) (2006) 473-484.

[10] J.E. Mills, Certain congruences on orthodox semigroups, Pacific J. Math. 64 (1976) 217-226. doi: 10.2140/pjm.1976.64.217

[11] F. Pastijn and M. Petrich, Congruences on regular semigroups, Trans. Amer. Math. Soc. 295 (2) (1986) 607-633. doi: 10.1090/S0002-9947-1986-0833699-3

[12] M.K. Sen and A.K. Bhuniya, On the left inversive semiring congruences on additive regular semirings, Journal of the Korea Society of Mathematical Education 12 (2005) 253-274.

[13] M.K. Sen, S. Ghosh and P. Mukhopadhyay, Congruences on inverse semirings, in: Algebras and Combinatorics (Hong Kong, 1997) (pp. 391-400). Springer, Singapore, 1999.

[14] M.K. Sen, S.K. Maity and K.P. Shum, Clifford semirings and generalized Clifford semirings. Taiwanese Journal of Mathematics 9 (3) (2005), 433-444.