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Torsion theories and corresponding radical and semisimple classes. (English) Zbl 0669.17007

Results for torsion theories and corresponding radical and semisimple classes are known (as they have been defined) from the papers of S. E. Dickson [Trans. Am. Math. Soc. 121, 223–235 (1966; Zbl 0138.01801)], W. G. Leavitt and R. Wiegandt [Rocky Mt. J. Math. 9, 259–271 (1979; Zbl 0421.17001)], R. Mlitz [Proc. Edinb. Math. Soc., II. Ser. 23, 37–41 (1980; Zbl 0414.17003)] and L. C. A. van Leeuwen and R. Wiegandt [Acta Math. Acad. Sci. Hung. 36, 37–47 (1980; Zbl 0466.17005)].
In this paper the authors continue to discuss, in the category \(Rng\) of not necessarily associative rings, the analogy between torsion theories and corresponding radical and semisimple classes, and give some new characterizations for them.
Reviewer: G. Tzintzis

MSC:

17A65 Radical theory (nonassociative rings and algebras)
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
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