Modules which are isomorphic to their factor modules. (English) Zbl 1266.13006
Let \(R\) be a commutative ring with identity. An infinite unitary \(R\)-module \(M\) is called homomorphically congruent (HC for short) if \(M/N\cong M\) for every submodule \(N\) of \(M\) such that \(|M/N| = |M|\). The authors prove some general results on HC modules, including HC module-theoretic characterizations of discrete valuation rings, almost Dedekind domains, and fields. Then they provide a characterization of the HC modules over a Dedekind domain. They close the paper with some open questions.
Reviewer: Siamak Yassemi (Tehran)
MSC:
| 13A99 | General commutative ring theory |
| 13C05 | Structure, classification theorems for modules and ideals in commutative rings |
| 13E05 | Commutative Noetherian rings and modules |
| 03E50 | Continuum hypothesis and Martin’s axiom |
Keywords:
almost Dedekind domain; Artinian module; Dedekind domain; discrete valuation ring; Noetherian module; strong limit cardinal; socle; uniserial moduleReferences:
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