published by Damascus University
in 2014
in Mathematics
and research's language is
العربية
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Abstract in English
Let R be a ring with identity.
The ain is to study some fundamental properties of a ring R when R is regular
or semi-potent and the radical Jacobson of R when R is semi-potent.
New results were obtained including necessary and sufficient conditions of R
to be regular or semi-potent. New substructures of R are studied and their
relationship with the total of R.
References used
Kasch. F: (1982). Modules and Rings. Academic Press
Kasch. F, Mader. A. (2004). Rings, Modules, and the Total. Front. Math., Birkhauser Verlag, Basel
Nicholson. W. K. (1975). I-Rings. Trans. Amer. Math. Soc.207, p.361-373