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Mapping of torsions and localizations of modules with the help of functors. (Russian) Zbl 0615.16004
This paper is a sequel of a previous paper of the author [ibid. 85, 83-95 (1985; Zbl 0604.16004)]. Let $${}_ RU_ S$$ be an arbitrary R-S bimodule, $$H=Hom_ R(U$$,-), $$T=U\otimes_ S$$- the pair of adjoint functors between R-Mod and S-Mod, and $$\alpha$$ : I(R)$$\to I(S)$$, $$\alpha$$ ’: I(S)$$\to I(R)$$ the mappings between the sets of all idempotent radicals of R-Mod and S-Mod considered in the above mentioned paper. The aim of the paper under review is to find conditions for which the mapping $$\alpha$$ resp. $$\alpha$$ ’ preserves torsion radicals resp. cotorsion radicals. The question when the functor H preserves localizations and the functor T preserves colocalizations is also investigated.
Reviewer: T.Albu
##### MSC:
 16Nxx Radicals and radical properties of associative rings 16S90 Torsion theories; radicals on module categories (associative algebraic aspects) 16B50 Category-theoretic methods and results in associative algebras (except as in 16D90) 18E40 Torsion theories, radicals
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