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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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