Torsion and Ortho-Slender Classes |
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Authors: | Radoslav M Dimitrić |
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Institution: | (1) DIBR, P.O. Box 382, Pittsburgh, PA 15230, USA |
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Abstract: | This paper generalizes a number of results obtained by Dimitrić in (Glas. Mat. 21(41):327–329, 1986; Proceedings of Hobart Conference on Rings, Modules and Radicals 1987, 204:41–50, Gordon and Breach, 1989) and Dimitrić and Goldsmith in (Glas. Mat. 23(43):241–246, 1988). The original papers were restricted to the category of Abelian groups and orthogonality was to the group of integers ℤ.
Here, we are in a general Abelian category with products and coproducts, with applications to module categories and further
to modules over PID’s. Another generalization is in replacing ℤ by an entire class of subobjects
of the underlying category. We examine properties of the torsion class
, Hom(T,C)=0} in relation to purity, direct summands and indecomposability as well as commutation with direct products, for example.
Of special interest are members of this class when
is a class of slender objects in the ground category; in this case, members of
are called ortho-slender objects. In a sense, ortho-slenderness represents complementary, if not dual, notion to slenderness.
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Keywords: | Slender objects Ortho-slender radical Ortho-slender object Ortho-slender class Torsion theory Torsion class Pure submodules Coslender object Preradicals Radicals |
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