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2011 | 31 | 2 | 147-158
Tytuł artykułu

Distributive lattices of t-k-Archimedean semirings

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A semiring S in 𝕊𝕃⁺ is a t-k-Archimedean semiring if for all a,b ∈ S, b ∈ √(Sa) ∩ √(aS). Here we introduce the t-k-Archimedean semirings and characterize the semirings which are distributive lattice (chain) of t-k-Archimedean semirings. A semiring S is a distributive lattice of t-k-Archimedean semirings if and only if √B is a k-ideal, and S is a chain of t-k-Archimedean semirings if and only if √B is a completely prime k-ideal, for every k-bi-ideal B of S.
Kategorie tematyczne
Rocznik
Tom
31
Numer
2
Strony
147-158
Opis fizyczny
Daty
wydano
2011
otrzymano
2010-07-17
poprawiono
2011-06-21
Twórcy
  • Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya, Hatgobindapur, Burdwan-713407, West Bengal, India
Bibliografia
  • [1] A.K. Bhuniya and K. Jana, Bi-ideals in k-regular and intra k-regular semirings, accepted for publication in Discuss. Math. General Algebra and Applications 31 (2011), 5-25.
  • [2] A.K. Bhuniya and T.K. Mondal, Distributive lattice decompositions of semirings with a semilattice additive reduct, Semigroup Forum 80 (2010), 293-301. doi: 10.1007/s00233-009-9205-6
  • [3] S. Bogdanovic and M. Ciric, Semilattice of Archimedean semigroups and completely π-regular semigroups I (survey article), Filomat(nis) 7 (1993), 1-40.
  • [4] S. Bogdanovic and M. Ciric, Chains of Archimedean semigroups (Semiprimary semigroups), Indian J. Pure and Appl. Math. 25 (1994), 229-235.
  • [5] M. Ciric and S. Bogdanovic, Semilattice decompositions of semigroups, Semigroup Forum (1996), 119-132. doi: 10.1007/BF02574089
  • [6] A.H. Clifford, Semigroups admitting relative inverses, Annals of Math. 42 (1941), 1037-1049. doi: 10.2307/1968781
  • [7] F. Kmet, Radicals and their left ideal analogues in a semigroup, Math. Slovaca 38 (1988), 139-145.
  • [8] M. Petrich, The maximal semilattice decomposition of a semigroup, Math. Zeitschr. 85 (1964), 68-82. doi: 10.1007/BF01114879
  • [9] M.S. Putcha, Semilattice decomposition of semigroups, Semigroup Forum 6 (1973), 12-34. doi: 10.1007/BF02389104
  • [10] T. Tamura, Another proof of a theorem concerning the greatest semilattice decomposition of a semigroup, Proc. Japan Acad. 40 (1964), 777-780. doi: 10.3792/pja/1195522562
  • [11] T. Tamura, On Putcha's theorem concerning semilattice of archimedean semigroups, Semigroup Forum 4 (1972), 83-86. doi: 10.1007/BF02570773
  • [12] T. Tamura, Note on the greatest semilattice decomposition of semigroups, Semigroup Forum 4 (1972), 255-261. doi: 10.1007/BF02570795
  • [13] T. Tamura and N. Kimura, On decomposition of a commutative semigroup, Kodai Math. Sem. Rep. 4 (1954), 109-112. doi: 10.2996/kmj/1138843534
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1179
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