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Tytuł artykułu

Semigroup of k-bi-ideals of a semiring with semilattice additive reduct

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Języki publikacji
EN
Abstrakty
EN
We associate a semigroup B(S) to every semiring S with semilattice additive reduct, namely the semigroup of all k-bi-ideals of S; and such semirings S have been characterized by this associated semigroup B(S). A semiring S is k-regular if and only if B(S) is a regular semigroup. For the left k-Clifford semirings S, B(S) is a left normal band; and consequently, B(S) is a semilattice if S is a k-Clifford semiring. Also we show that the set Bm(S) of all minimal k-bi-ideals of S forms a rectangular band and Bm(S) is a bi-ideal of the semigroup B(S).
Wydawca
Rocznik
Strony
119--128
Opis fizyczny
Bibliogr. 16 poz.
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, H. J. Weinert, On k-regular semirings, Bull. Calcutta Math. Soc. 88 (1996), 141–144.
  • [2] A. K. Bhuniya, Structure and characteristics of left k-Clifford semirings, Asian-European J. Math. 6(4) (2013).
  • [3] A. K. Bhuniya, K. Jana, Bi-ideals in k-regular and intra k-regular semirings, Discuss. Math. Gen. Algebra Appl. 31 (2011), 5–23.
  • [4] A. K. Bhuniya, K. Jana, Minimal k-bi-ideals and strong quasi k-ideals in a semirings, communicated.
  • [5] S. Bourne, The Jacobson radical of a semiring, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 163–170.
  • [6] R. H. Good, D. R. Hughes, Associated groups for semigroup, Bull. Amer. Math. Soc. 58 (1952), 624–625.
  • [7] U. Hebisch, H. J. Weinert, Semirings: Algebric Theory and Applications in Computer Science, World Scientific, Singapore, 1998.
  • [8] J. M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford, 1995.
  • [9] 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.
  • [10] G. L. Litvinov, V. P. Maslop, The correspondence principle for idempotent calculas and some computer applications, in Idempotency, J. Gunawardena (Editor), Cambridge Univ. Press, Cambridge, 1998, 420–443.
  • [11] G. L. Litvinov, V. P. Maslop, G. B. Shpiz, Idempotent functional analysis, Mat. Zametki 69(5) (2001), 758–797.
  • [12] G. L. Litvinov, V. P. Maslop, A. N. Sobolevskii, Idempotent Mathematics and Interval analysis, The Erwin Schrödinger International Institute for Mathematical Physics, Vienna, 1998.
  • [13] M. K. Sen, A. K. Bhuniya, Completely k-regular semirings, Bull. Calcutta Math. Soc. 97(5) (2005), 455–466.
  • [14] M. K. Sen, A. K. Bhuniya, On additive idempotent k-Clifford semirings, Southeast Asian Bull. Math. 32 (2008), 1149–1159.
  • [15] M. K. Sen, A. K. Bhuniya, On semirings whose additive reduct is a semilattice, Semigroup Forum 82 (2011), 131–140.
  • [16] 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.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5cb28b57-3924-43c5-b9be-d7c1f4518860
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