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2013 | 33 | 1 | 85-93
Tytuł artykułu

On k-radicals of Green's relations in semirings with a semilattice additive reduct

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.
Kategorie tematyczne
Rocznik
Tom
33
Numer
1
Strony
85-93
Opis fizyczny
Daty
wydano
2013
otrzymano
2013-02-04
poprawiono
2013-02-26
Twórcy
  • Department of Mathematics Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya Hatgobindapur, Burdwan - 713407 West Bengal, India
  • Department of Mathematics Visva-Bharati, Santiniketan Bolpur - 731235, West Bengal, India
Bibliografia
  • [1] A.K. Bhuniya, On the additively regular semirings, Ph.D Thesis, University of Calcutta, 2009.
  • [2] A.K. Bhuniya and K. Jana, Bi-ideals in k-regular and intra k-regular semirings, Discuss. Math. General Algebra and Applications 31 (2011) 5-25. ISSN 2084-0373
  • [3] 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
  • [4] A.K. Bhuniya and T.K. Mondal, Semirings which are distributive lattices of left k-Archimedean semirings, Semigroup Forum (to appear). ISSN 1432-2137
  • [5] A.K. Bhuniya and T.K. Mondal, Semirings which are distributive lattices of k-simple semirings, Southeast Asian Bulletin of Mathematics 36 (2012) 309-318. ISSN 0129-2021
  • [6] S. Bogdanović and M. Ćirić, A note on radicals of Green's relations, PU.M.A 7 (1996) 215-219. ISSN 1218-4586
  • [7] S. Bogdanović and M. Ćirić, A note on left regular semigroups Publ. Math. Debrecen 48 (3-4) (1996) 285-291. ISSN 0033-3883
  • [8] A.H. Clifford and G.B. Preston, The algebraic theory of semigroups I, Amer. Math. Soc., 1977. ISBN 0-8218-0271-2
  • [9] A.H. Clifford, Semigroups admitting relative inverses, Ann. Math. 42 (1941) 1037-1049. ISSN 1939-0980
  • [10] U. Hebisch and H.J. Weinert, Semirings. Algebraic Theory and Applications in Computer Science (Singapore, World Scientific, 1998). ISBN 981-02-3601-8
  • [11] J.M. Howie, Fundamentals of semigroup theory (Clarendon, Oxford, 1995). Reprint in 2003. ISBN 0-19-851194-9
  • [12] G.L. Litvinov and V.P. Maslov, The Correspondence principle for idempotent calculus and some computer applications, in: Idempotency, J. Gunawardena (Editor), (Cambridge, Cambridge Univ. Press, 1998) 420-443.
  • [13] G.L. Litvinov, V.P. Maslov and A.N. Sobolevskii, Idempotent Mathematics and Interval Analysis, Preprint ESI 632, The Erwin Schrödinger International Institute for Mathematical Physics, Vienna, 1998; e-print: http://www.esi.ac.at and http://arXiv.org,math.Sc/9911126.
  • [14] T.K. Mondal, Distributive lattices of t-k-Archimedean semirings, Discuss. Math. General Algebra and Applications 31 (2011), 147-158. doi: 10.7151/dmgaa.1179
  • [15] T.K. Mondal and A.K. Bhuniya, Semirings which are distributive lattices of t-k-simple semirings, submitted.
  • [16] M.K. Sen and A.K. Bhuniya, On semirings whose additive reduct is a semilattice, Semigroup forum 82 (2011) 131-140. doi: 10.1007/s00233-010-9271-9
  • [17] L.N. Shevrin, Theory of epigroups I, Mat. Sbornic 185 (8) (1994) 129-160. ISSN 1468-4802
  • [18] 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. ISSN 1088-9485
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1198
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