MODULES WHOSE MAXIMAL SUBMODULES ARE SUPPLEMENTS

Key Findings & Data:For a locally projective module, we prove that every maximal submodule is a direct summand if and only if it is semisimple and projective.

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Conclusion & Impact:We give a complete characterization of the modules whose maximal submodules are supplements over Dedekind domains

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Locally projective module · Supplement submodule · 2000 AMS Classification: 13 C 05

Abstract

We study modules whose maximal submodules are supplements (direct summands). For a locally projective module, we prove that every maximal submodule is a direct summand if and only if it is semisimple and projective. We give a complete characterization of the modules whose maximal submodules are supplements over Dedekind domains

Keywords

Locally projective module Supplement submodule 2000 AMS Classification: 13 C 05

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Cite This Article

Büyükasik, E., Pusat-yilmaz, D. (2010). MODULES WHOSE MAXIMAL SUBMODULES ARE SUPPLEMENTS. Hacettepe Journal of Mathematics and Statistics, Volume: 39 Issue: 4. https://ajindex.com/articles/1403682

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