On γ-Clean Rings
DOI:
https://doi.org/10.25271/2017.5.3.398Keywords:
γ-clean rings, r-clean rings, clean rings and γ-regular rings, regular ringsAbstract
In this paper we introduce the concept of -clean ring and we discuss some relations between - clean ring and other rings with explaining by some examples. Also, we give some basic properties of it.
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References
Abdul-Jabbar, A. M., " On γ-regular rings and generalized γ-regular rings", Accepted J. Duhok Univ.
Ashrafi, N. and Nasibi, E., (2013), "Rings in which elements are the sum of an idempotent and a regular element", J. Bulletin Iranian Mathematical Society, Vol.39, No.3, pp.579-588.
Ashrafi, N. and Nasibi, E., (2013), "r-Clean Rings" to appear in Mathematical Reports, Vol.15(65), no.2.
Anderson, D. D. and Camillo, V. P., (2002), "Commutative Rings whose Elements are a sum of a unit and idempotent", J. Comm. Algebra, Vol.30, No.7, pp.3327-3336.
Esa, Sh. S., (2010), "A Study of some types of Strongly regular rings", M. Sc. Thesis, Mosul University.
Esa, Sh. S., (2015), "On γVNL-ring", J. Duhok Univ. (Pure and Eng. Sciences), Vol.18, No.1, pp.93-96.
Lam, T. Y., (2000), "Exercises in Classical Ring Theory", Springer-Verlag, New York Berlin Heidelberg,.
Mohammad, A. J. and Salih, S. M., (2006), "On γ-regular rings", J. Edu. Sci., Vol.18, No.4, pp.118-139.
Nicholson, W. K., (1977), "Lifting idempotent and exchange rings", Trans. Amer. Math. Soc. Vol.229, pp.269-278.
Von Neumann, J. (1936),"On regular rings", J. Princeton N., Vol.22, pp.707-713.
Ashrafi, N. and Nasibi, E., (2013), "Rings in which elements are the sum of an idempotent and a regular element", J. Bulletin Iranian Mathematical Society, Vol.39, No.3, pp.579-588.
Ashrafi, N. and Nasibi, E., (2013), "r-Clean Rings" to appear in Mathematical Reports, Vol.15(65), no.2.
Anderson, D. D. and Camillo, V. P., (2002), "Commutative Rings whose Elements are a sum of a unit and idempotent", J. Comm. Algebra, Vol.30, No.7, pp.3327-3336.
Esa, Sh. S., (2010), "A Study of some types of Strongly regular rings", M. Sc. Thesis, Mosul University.
Esa, Sh. S., (2015), "On γVNL-ring", J. Duhok Univ. (Pure and Eng. Sciences), Vol.18, No.1, pp.93-96.
Lam, T. Y., (2000), "Exercises in Classical Ring Theory", Springer-Verlag, New York Berlin Heidelberg,.
Mohammad, A. J. and Salih, S. M., (2006), "On γ-regular rings", J. Edu. Sci., Vol.18, No.4, pp.118-139.
Nicholson, W. K., (1977), "Lifting idempotent and exchange rings", Trans. Amer. Math. Soc. Vol.229, pp.269-278.
Von Neumann, J. (1936),"On regular rings", J. Princeton N., Vol.22, pp.707-713.
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Published
2017-09-30
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Science Journal of University of Zakho
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Copyright (c) 2017 Shaimaa S. Esa, Hewa S. Faris
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How to Cite
Esa, S. S., & Faris, H. S. (2017). On γ-Clean Rings. Science Journal of University of Zakho, 5(3), 285-287. https://doi.org/10.25271/2017.5.3.398
