Volume 37 | Number 4 | Year 2016 | Article Id. IJMTT-V37P532 | DOI : https://doi.org/10.14445/22315373/IJMTT-V37P532
An element of a ring R is clean if it is the sum of an idempotent and a unit. A ring R is called clean if each of its elements is clean. In this paper we define a ring is G-Clean if each of its elements is the sum of a G-regular and an idempotent element. Finally we investigate some properties of G-clean rings.
[1] Anderson, D. F., A. Badawi.(2012) Von Neumann regular and related elements incommutative rings.Algebra Colloq,19, 1017-1041.
[2] Ara, P. (1996). -regular rings have stable rangeone Proc. Amer. Math. Soc., 124, No. 11, 3293-3298.
[3] Azumaya, G. (1954). Strongly -regular rings. J. Fac. Sci. Hokkaido Univ.,13. 34-39.
[4] Badawi, A. (1993). Semicommutative -regular rings Commun. Algebra, 22, No. 1, 151-157.
[5] Badawi, A.(1997).Abelian -regular rings Commun. Algebra, 25, No. 4, 1009-1021.
[6] Burgess, W. D., Menal (1988). Strongly -regular rings and homomorphisms into them Commun. Algebra, 16, 1701-1725.
[7] Camillo, V.,Xiao, Y. (1994).Regular rings Commun. Algebra, 22, No. 10, 4095-4112.
[8] Chacron, M. (1969).Algebraic rings.Bull. Austral. Math. Soc., 1, 385-389.
[9] Chin,A. Y. M., Chen, H. V. (2002) On strongly -regular, Southeast Asian Bulletin of Mathematices, 26, 387-390.
[10] Goodearl, K. R. (1979). Von Neumann regular rings.Pitman, London.
[11] Gupta, V. (1984).Generalization of strongly regular rings.Acta Math. Hung., 43, 57-61.
[12] Han, J.,Nicholson, W. K. (2001). Extensions of clean rings. Comm. Algebra, 29 (6),2589-2595.
[13] Hirano, Y. (1978). Studies on strongly -regular rings.Math. J. Okayama Univ., 20, No. 2, 141-149.
[14] Hirano, Y. (1985). -regular rings with involution.Math. J. Okayama Univ., 27, 45-47.
[15] Hirano, Y., J.Park, J. P.(1993).Self-injective strongly -regularrings.Commun.Algebra, 21, No. 1, 85-91.
[16] Lam, T. Y.(1991) A first course in Non-commutative rings.Gradate texts in Mathematics, No. 131,springer-verlag.
[17] Ohori, M. (1997). Strongly -regular rings and periodic rings.Math. J. Okayama Univ., 19, No. 2, 123-127.
[18] Safari sabet, Sh. A., Farmani, M., Karami, M. (2013).On strongly commuting regular rings J. Basic. Appl. Sci. Res, 3. No. 2
[19] Safari sabet.Sh. A Karami, M. (2014). -regular and strongly -regular Rings.IJONS. 26(5), 1953-1958.
[20] Steger. A. 1966 factorization in -regular rings.Canad. J. Math., 18, 307-313.
[21] Xue, W.(1993).Three questions on strongly -regular rings and regular rings. Commun. Algebra21, No. 2, 699-704.
[22] Yamini, A. H.,Safari Sabet, Sh. A. 2004 Commuting regular rings.Int. J. Appl. Math, 14(4), 357-364.
[23] Yu, H. P. (1995).On strongly -regular rings of stable rangeone.Bull. Austral. Math.Soc., 51, No. 3, 433-437.
Shaaban Ali SafariSabet, MarziehFarmani, "G-Clean rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 37, no. 4, pp. 234-237, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V37P532