Rings Graded By a Generalized Group

Farzad Fatehi; Mohammad Reza Molaei

Topological Algebra and its Applications (2014)

  • Volume: 2, Issue: 1, page 24-31, electronic only
  • ISSN: 2299-3231

Abstract

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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..

How to cite

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Farzad Fatehi, and Mohammad Reza Molaei. "Rings Graded By a Generalized Group." Topological Algebra and its Applications 2.1 (2014): 24-31, electronic only. <http://eudml.org/doc/269616>.

@article{FarzadFatehi2014,
abstract = {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..},
author = {Farzad Fatehi, Mohammad Reza Molaei},
journal = {Topological Algebra and its Applications},
keywords = {Completely simple semigroup; Grading; Graded ring; Maximal ideal; Homogeneous ideal; completely simple semigroups; semigroup gradings; semigroup graded rings; maximal ideals; homogeneous ideals},
language = {eng},
number = {1},
pages = {24-31, electronic only},
title = {Rings Graded By a Generalized Group},
url = {http://eudml.org/doc/269616},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Farzad Fatehi
AU - Mohammad Reza Molaei
TI - Rings Graded By a Generalized Group
JO - Topological Algebra and its Applications
PY - 2014
VL - 2
IS - 1
SP - 24
EP - 31, electronic only
AB - 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..
LA - eng
KW - Completely simple semigroup; Grading; Graded ring; Maximal ideal; Homogeneous ideal; completely simple semigroups; semigroup gradings; semigroup graded rings; maximal ideals; homogeneous ideals
UR - http://eudml.org/doc/269616
ER -

References

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  1. [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. Zbl1064.20065
  2. [2] Bhavnagri B. (2011). Representational Consistency of Group Rings, Journal of Mathematics Research, 3, 3, 89-95. Zbl1263.03035
  3. [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] Zbl1248.17008
  4. [4] Fatehi F., Molaei M.R. (2012). On Completely Simple Semigroups, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 28, 95-102. Zbl1274.20065
  5. [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. [6] Howie J.M. (1995). Fundamental of semigroup theory, Clarendon Press. Zbl0835.20077
  7. [7] Molaei M.R. (1999). Generalized groups, Bul. Inst. Politeh. Din Jasi, Sect. I. Mat. Mec. Teor. Fiz. XLV (XLIX) 3-4, 21-24. Zbl1002.20038
  8. [8] Molaei M.R. (2005). Mathematical structures based on completely simple semigroups, Monographs in Mathematics, Hadronic Press, 1-90. Zbl1149.22002
  9. [9] Molaei M.R., Farhangdost M.R. (2006). Upper top spaces, Applied Sciences, 8, 128-131. Zbl1104.22002
  10. [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. Zbl1185.22015
  11. [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. Zbl1101.37015
  12. [12] Rees D. (1940). On semigroups, Proceedings of the Cambridge Philosophical Society 36, 387-400. [Crossref][WoS] Zbl66.1207.01

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