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- W2022083482 abstract "Let R be commutative ring with identity and let M be an infinite unitary R-module. Call M homomorphically congruent (HC for short) provided M/N ≅ M for every submodule N of M for which |M/N| = |M|. In this article, we study HC modules over commutative rings. After a fairly comprehensive review of the literature, several natural examples are presented to motivate our study. We then prove some general results on HC modules, including HC module-theoretic characterizations of discrete valuation rings, almost Dedekind domains, and fields. We also provide a characterization of the HC modules over a Dedekind domain, extending Scott's classification over ℤ in [22]. Finally, we close with some open questions." @default.
- W2022083482 created "2016-06-24" @default.
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- W2022083482 date "2013-04-22" @default.
- W2022083482 modified "2023-09-26" @default.
- W2022083482 title "Modules Which are Isomorphic to Their Factor Modules" @default.
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- W2022083482 doi "https://doi.org/10.1080/00927872.2011.625561" @default.
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