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Tytuł artykułu

Rings Graded By a Generalized Group

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups. We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. We prove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deduce a characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if R is a Noetherian graded ring, then each summand of it is also a Noetherian module..
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2013-04-30
zaakceptowano
2014-08-15
online
2014-11-18
Twórcy
  • Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111 Kerman, Iran
  • Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111 Kerman, Iran, mrmolaei@uk.ac.ir
Bibliografia
  • [1] Araujo J., Konieczny J. (2002). Molaei’s generalized groups are completely simple semigroups, Bul. Inst. Politeh. Jassy,Sect. I. Mat. Mec. Teor. Fiz. 48(52) 1-2, 1-5.
  • [2] Bhavnagri B. (2011). Representational Consistency of Group Rings, Journal of Mathematics Research, 3, 3, 89-95.
  • [3] Draper C., Elduque A., Martin-Gonzalez C. (2011). Fine gradings on exceptional simple Lie superalgebras, InternationalJournal of Mathematics 22 (12), 1823-1855.[WoS][Crossref]
  • [4] Fatehi F., Molaei M.R. (2012). On Completely Simple Semigroups, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis,28, 95-102.
  • [5] Fatehi F., Molaei M.R. (2012), Some Algebraic Properties of Generalized Rings, To appear in Analele Stiintifice Ale Universitatii"AL.I. CUZA" DIN IASI (S.N.) Matematica.
  • [6] Howie J.M. (1995). Fundamental of semigroup theory, Clarendon Press.
  • [7] Molaei M.R. (1999). Generalized groups, Bul. Inst. Politeh. Din Jasi, Sect. I. Mat. Mec. Teor. Fiz. XLV (XLIX) 3-4, 21-24.
  • [8] Molaei M.R. (2005). Mathematical structures based on completely simple semigroups, Monographs in Mathematics,Hadronic Press, 1-90.
  • [9] Molaei M.R., Farhangdost M.R. (2006). Upper top spaces, Applied Sciences, 8, 128-131.
  • [10] Molaei M.R., Farhangdost M.R. (2009). Lie algebras of a class of top spaces, Balkan Journal of Geometry and Its Applications14 (1), 46-51.
  • [11] Molaei M.R., Khadekar G.S., Farhangdost M.R. (2006). On top spaces, Balkan Journal of Geometry and Its Applications11 (1), 101-106.
  • [12] Rees D. (1940). On semigroups, Proceedings of the Cambridge Philosophical Society 36, 387-400.[Crossref][WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_taa-2014-0005
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