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2011 | 31 | 1 | 5-23
Tytuł artykułu

Bi-ideals in k-regular and intra k-regular semirings

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Here we introduce the k-bi-ideals in semirings and the intra k-regular semirings. An intra k-regular semiring S is a semiring whose additive reduct is a semilattice and for each a ∈ S there exists x ∈ S such that a + xa²x = xa²x. Also it is a semiring in which every k-ideal is semiprime. Our aim in this article is to characterize both the k-regular semirings and intra k-regular semirings using of k-bi-ideals.
Kategorie tematyczne
Rocznik
Tom
31
Numer
1
Strony
5-23
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-04-06
poprawiono
2010-01-18
Twórcy
  • Department of Mathematics Visva-Bharati, Santiniketan-731235, India
autor
  • Department of Mathematics, Katwa College Katwa-713130, India
Bibliografia
  • [1] M.R. Adhikari, M.K. Sen and H.J. Weinert, On k-regular semirings, Bull.Cal.Math.Soc. 88 (1996), 141-144.
  • [2] S. Bourne, The Jacobson radical of a semiring, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 163-170. doi: 10.1073/pnas.37.3.163
  • [3] R. Chinram and K. Tinpun, A note on minimal bi-ideals in ordered Γ-semigroups, International Math. Forum 4 (1) (2009), 1-5.
  • [4] R.A. Good and D.R. Hughes, Associated groups for a semigroup, Bull. Amer. Math. Soc. 58 (1952), 624-625.
  • [5] M. Henricksen, Ideals in semirings with commutative addition, Amer. Math. Soc. Notices (1958), 321.
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  • [7] K.M. Kapp, On bi-ideals and quasi-ideals in semigroups, Publ. Math. Debrecan 16 (1969), 179-185.
  • [8] K.M. Kapp, Bi-ideals in associative rings and semigroups, Acta. Sci. Math. 33 (1972), 307-314.
  • [9] N. Kehayopulu, J.S. Ponizovskii and M. Tsingelis, Bi-ideals in ordered semigroups and ordered groups, J. Math. Sci. 112 (4) (2002), 4353-4354. doi: 10.1023/A:1020347003781
  • [10] Y. Kemprasit, Quasi-ideals and bi-ideals in semigroups and rings, Proceedings of the International Conference on Algebra and its Applicatipns (2002), 30-46.
  • [11] S. Lajos, On (m, n)-ideals of semigroups, Abstract of Second Hunger. Math. Congress I (1960), 42-44.
  • [12] S. Lajos, On the bi-ideals in semigroups, Proc. Japan. Acad. 45 (1969), 710-712. doi: 10.3792/pja/1195520625
  • [13] S. Lajos, On generalized bi-ideals in semigroups, Coll. Math. Soc. Janos Bolyai, Algebraic Theory of semigroups (G. Polak, Ed.), North-Holland 20 (1979), 335-340.
  • [14] S. Lajos and F. Szaaz, Bi-ideals in associative rings, Acta. Sci. Math. 32 (1971), 185-193.
  • [15] S. Li and Y. He, On semigroups whose bi-ideals are strongly prime, International J. Algebra 1 (6) (2007), 263-268.
  • [16] M. M. Miccoli, Bi-ideals in regular semigroups and orthogroups, Acta. Math. Hung. 47 (1-2) (1986), 3-6. doi: 10.1007/BF01949118
  • [17] J.V. Neumann, On regular rings, Proc. Nat. Acad. Sci. USA 22 (1936), 707-713. doi: 10.1073/pnas.22.12.707
  • [18] M.K. Sen and A.K. Bhuniya, Completely k-regular semirings, Bull. Cal. Math. Soc. 97 (2005), 455-466.
  • [19] M.K. Sen and A.K. Bhuniya, On Additive Idempotent k-Clifford Semirings, Southeast Asian Bulletin of Mathematics 32 (2008), 1149-1159.
  • [20] M.K. Sen and A.K. Bhuniya, On semirings whose additive reduct is semilattice, Communicated.
  • [21] X.Z. Xu and J.Y. Ma, A note on minimal bi-ideals in ordered semigroups, SEA Bull. Math. 27 (2003), 149-154.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1172
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