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Modules semicocritical with respect to a torsion theory and their applications

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Abstract

The concepts of primitive ideal and semicocritical module with respect to a torsion theory are studied and related to the structure of torsionfree injective modules. Applications are made to the study of (1) composition series with respect to a torsion theory and (2) the structure of endomorphism rings of torsionfree modules. These results are natural generalizations of the properties of certain modules over (noetherian) rings with Krull dimension.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    Mark L. Teply

  2. Department of Mathematics, University of Wisconsin, 53201, Milwaukee, WI, USA

    Mark L. Teply

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  1. Mark L. Teply
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Teply, M.L. Modules semicocritical with respect to a torsion theory and their applications. Israel J. Math. 54, 181–200 (1986). https://doi.org/10.1007/BF02764941

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  • DOI: https://doi.org/10.1007/BF02764941

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