# The Clifford semiring congruences on an additive regular semiring

Discussiones Mathematicae - General Algebra and Applications (2014)

- Volume: 34, Issue: 2, page 143-153
- ISSN: 1509-9415

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topA.K. Bhuniya. "The Clifford semiring congruences on an additive regular semiring." Discussiones Mathematicae - General Algebra and Applications 34.2 (2014): 143-153. <http://eudml.org/doc/270704>.

@article{A2014,

abstract = {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.},

author = {A.K. Bhuniya},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {additive regular semiring; skew-ring; trace; kernel; Clifford congruence},

language = {eng},

number = {2},

pages = {143-153},

title = {The Clifford semiring congruences on an additive regular semiring},

url = {http://eudml.org/doc/270704},

volume = {34},

year = {2014},

}

TY - JOUR

AU - A.K. Bhuniya

TI - The Clifford semiring congruences on an additive regular semiring

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2014

VL - 34

IS - 2

SP - 143

EP - 153

AB - 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.

LA - eng

KW - additive regular semiring; skew-ring; trace; kernel; Clifford congruence

UR - http://eudml.org/doc/270704

ER -

## References

top- [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 Zbl0486.16026
- [2] R. Feigenbaum, Kernels of regular semigroup homomorphisms. Doctoral Dissertation (University of South Carolina, 1975). Zbl0343.20033
- [3] R. Feigenbaum, Regular semigroup congruences, Semigroup Forum 17 (1979) 373-377. doi: 10.1007/BF02194336 Zbl0433.20043
- [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 Zbl0948.16036
- [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 Zbl0316.16039
- [7] J.M. Howie, Fundamentals of semigroup theory (Clarendon, Oxford, 1995). Reprint in 2003. Zbl0835.20077
- [8] D.R. LaTorre, The least semilattice of groups congruence on a regular semigroup, Semigroup Forum 27 (1983) 319-329. doi: 10.1007/BF02572745 Zbl0524.20039
- [9] S.K. Maity, Congruences on additive inverse semirings, Southeast Asian Bull. Math. 30 (3) (2006) 473-484. Zbl1122.16040
- [10] J.E. Mills, Certain congruences on orthodox semigroups, Pacific J. Math. 64 (1976) 217-226. doi: 10.2140/pjm.1976.64.217 Zbl0358.20075
- [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 Zbl0599.20095
- [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. Zbl1139.16306
- [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. Zbl0980.16041
- [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. Zbl1091.16028

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