Rings Graded By a Generalized Group

• Autorzy: Farzad Fatehi , Mohammad Reza Molaei
• 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..

Słowa kluczowe

EN

Completely simple semigroup; Grading; Graded ring; Maximal ideal; Homogeneous ideal

Kategorie tematyczne

• 16W99: None of the above, but in this section
• 13A99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2013-04-30

zaakceptowano

2014-08-15

online

2014-11-18

Twórcy

autor

Farzad Fatehi

• Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111 Kerman, Iran

autor

Mohammad Reza Molaei

• Department of Mathematics, Shahid Bahonar University of Kerman, 76169-14111 Kerman, Iran

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, International Journal 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 Applications 14 (1), 46-51.
• [11] Molaei M.R., Khadekar G.S., Farhangdost M.R. (2006). On top spaces, Balkan Journal of Geometry and Its Applications 11 (1), 101-106.
• [12] Rees D. (1940). On semigroups, Proceedings of the Cambridge Philosophical Society 36, 387-400. [Crossref][WoS]

Identyfikatory

DOI

10.2478/taa-2014-0005