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2014 | 34 | 2 | 143-153
Tytuł artykułu

The Clifford semiring congruences on an additive regular semiring

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Kategorie tematyczne
Rocznik
Tom
34
Numer
2
Strony
143-153
Opis fizyczny
Daty
wydano
2014
otrzymano
2013
poprawiono
2014-05-05
poprawiono
2014-07-30
Twórcy
autor
  • Department of Mathematics, Visva-Bharati, Santiniketan-731235, West Bengal, India
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1219
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