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On Kulikov’s theorem. (English) Zbl 0592.16017
Let R be a ring with identity element, and let \(\tau\) be a torsion theory for R-mod. The concept of height for abelian groups is generalized to R- modules, where \(\tau\) becomes the analogue for the usual torsion for abelian groups. After a number of technical properties of height are established, a version of Kulikov’s Theorem for abelian groups is established for a nice class of R-modules. This paper should be a basis for further development of abelian group theory results to a torsion theoretic setting for special classes of R-modules.
Reviewer: M.L.Teply

MSC:
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
16D80 Other classes of modules and ideals in associative algebras
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