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2014 | 34 | 1 | 27-43
Tytuł artykułu

Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Here we introduce the notion of strong quasi k-ideals of a semiring in SL⁺ and characterize the semirings that are distributive lattices of t-k-simple(t-k-Archimedean) subsemirings by their strong quasi k-ideals. A quasi k-ideal Q is strong if it is an intersection of a left k-ideal and a right k-ideal. A semiring S in SL⁺ is a distributive lattice of t-k-simple semirings if and only if every strong quasi k-ideal is a completely semiprime k-ideal of S. Again S is a distributive lattice of t-k-Archimedean semirings if and only if √Q is a k-ideal, for every strong quasi k-ideal Q of S.
Kategorie tematyczne
Rocznik
Tom
34
Numer
1
Strony
27-43
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-04-26
poprawiono
2013-10-07
Twórcy
  • Department of Mathematics, Visva-Bharati, Santiniketan-731235, India
autor
  • Department of Mathematics, Katwa College, Katwa-713130, India
Bibliografia
  • [1] A.K. Bhuniya and K. Jana, Bi-ideals in k-regular and intra k-regular semirings, Discuss. Math. Gen. Alg. and Appl. 31 (2011) 5-23. doi: 10.7151/dmgaa.1172.
  • [2] C. Donges, On quasi ideals of semirings, Int. J. Math. and Math. Sci. 17(1) (1994) 47-58. doi: 10.1155/S0161171294000086.
  • [3] A.K. Bhuniya and T.K. Mondal, Distributive lattice decompositions of semirings with semilattice additive reduct, Semigroup Forum 80 (2010) 293-301. doi: 10.1007/s00233-009-9205-6.
  • [4] A.K. Bhuniya and T.K. Mondal, On the least distributive lattice congruence on semirings, communicated.
  • [5] S.M. Bogdanović, M.D. Ćirić, and Ž. Lj. Popović, Semilattice Decompositions of Semigroups (University of Niš, Faculty of Economics, 2011).
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  • [11] K. Jana, Quasi-k-ideals in k-regular and intra k-regular semirings, Pure Math. Appl. 22(1) (2011) 65-74.
  • [12] K. Jana, k-bi-ideals and quasi k-ideals in k-Clifford and left k-Clifford semirings, Southeast Asian Bull. Math. 37 (2013) 201-210.
  • [13] V.N. Kolokoltsov and V.P. Maslov, Idempotent Analysis and Its Applications (Kluwer Academic, Dordrecht, 1997).
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  • [17] T.K. Mondal, Distributive lattice of t-k-Archimedean semirings, Discuss. Math. Gen. Alg. and Appl. 31 (2011) 147-158. doi: 10.7151/dmgaa.1179.
  • [18] T.K. Mondal and A.K. Bhuniya, Semirings which are distributive lattices of t-k-simple semirings, communicated.
  • [19] M.K. Sen and A.K. Bhuniya, On additive idempotent k-regular semirings, Bull. Cal. Math. Soc. 93 (2001) 371-384.
  • [20] O. Steinfeld, Quasi-ideals in Rings and Regular Semigroups (Akademiai Kiado, Budapest, 1978).
  • [21] H.S. Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934) 914-920. doi: 10.1090/S0002-9904-1934-06003-8.
  • [22] H.J. Weinert, on quasi-ideals in rings, Acta Math. Hung. 43 (1984) 85-99. doi: 10.1007/BF01951330.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1213
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