# 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

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topFarzad 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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- [2] Bhavnagri B. (2011). Representational Consistency of Group Rings, Journal of Mathematics Research, 3, 3, 89-95. Zbl1263.03035
- [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] Fatehi F., Molaei M.R. (2012). On Completely Simple Semigroups, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 28, 95-102. Zbl1274.20065
- [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. Zbl0835.20077
- [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] Molaei M.R. (2005). Mathematical structures based on completely simple semigroups, Monographs in Mathematics, Hadronic Press, 1-90. Zbl1149.22002
- [9] Molaei M.R., Farhangdost M.R. (2006). Upper top spaces, Applied Sciences, 8, 128-131. Zbl1104.22002
- [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] 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] Rees D. (1940). On semigroups, Proceedings of the Cambridge Philosophical Society 36, 387-400. [Crossref][WoS] Zbl66.1207.01

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