Extending modules, exact covers and projective covers (Q2771176)
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scientific article; zbMATH DE number 1705274
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extending modules, exact covers and projective covers |
scientific article; zbMATH DE number 1705274 |
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25 June 2002
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extending modules
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quasi-injective modules
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projective covers
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Extending modules, exact covers and projective covers (English)
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The authors show that a module \(M\) is an extending module if and only if it is C-quasi-injective, i.e., given a closed submodule \(N\), every homomorphism \(f\colon N\to M\) can be extended to some \(g\) in \(\text{End}(M)\). A generalization of Schur's famous lemma is also given. A result of the reviewer [Bull. Aust. Math. Soc. 49, No. 1, 35-45 (1994; Zbl 0808.16006)] is extended.
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