Relations between ΛBV and BV(p(n) ↑∞) Classes of Functions |
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Authors: | U Goginava |
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Institution: | (1) Discipline of Mathematics, University of Tasmania, GPO Box 252-37, Hobart, Tasmania, 001, Australia;(2) School of Mathematical and Decision Sciences, Central Queensland University, Rockhampton, Queensland, 4702, Australia |
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Abstract: | The base radical class L
b(X), generated by a class X was introduced in 12]. It consists of those rings whose nonzero homomorphic images have nonzero accessible subrings in X. When X is homomorphically closed, L
b(X) is the lower radical class defined by X, but otherwise X may not be contained in L
b(X). We prove that for a hereditary radical class L with semisimple class S(R), L
b(S(R)) is the class of strongly R-semisimple rings if and only if R is supernilpotent or subidempotent. A number of further examples of radical classes of the form L
b(X) are discussed.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | associative rings base radical class |
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