On 𝒦-Nonsingular Modules and Applications |
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| Authors: | S Tariq Rizvi Cosmin S Roman |
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| Institution: | 1. Department of Mathematics , Ohio State University , Lima, Ohio, USA rizvi.1@osu.edu;3. Department of Mathematics , Ohio State University , Lima, Ohio, USA |
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| Abstract: | We introduce the notion of 𝒦-nonsingularity of a module and show that the class of 𝒦-nonsingular modules properly contains the classes of nonsingular modules and of polyform modules. A necessary and sufficient condition is provided to ensure that this property is preserved under direct sums. Connections of 𝒦-nonsingular modules to their endomorphism rings are investigated. Rings for which all modules are 𝒦-nonsingular are precisely determined. Applications include a type theory decomposition for 𝒦-nonsingular extending modules and internal characterizations for 𝒦-nonsingular continuous modules which are of type I, type II, and type III, respectively. |
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| Keywords: | Baer modules Continuous modules Endomorphism rings Extending modules Nonsingular modules Type theory decomposition |
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