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Height relative to a torsion theory. (English) Zbl 0589.16021
Ring theory, Proc. Int Conf., Antwerp/Belg. 1985, Lect. Notes Math. 1197, 178-184 (1986).
[For the entire collection see Zbl 0583.00007.]
Let R be a ring and let $$\tau$$ be a torsion theory of left R-modules. By replacing simple and uniserial modules with $$\tau$$-cocritical and $$\tau$$- uniserial modules, respectively, a height theory for modules is obtained as a generalization of the height theory of S. Singh [Can. J. Math. 27, 867-883 (1975; Zbl 0275.16006)]. Some applications to the decomposition of modules ”modulo $$\tau$$ ” are discussed.
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