Semi-chain module

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A module which can be decomposed as a direct sum of chain submodules (see Chain module). All left $R$-modules are semi-chain modules if and only if $R$ is a generalized uniserial ring.


A chain module is also called a uniserial module; correspondingly, a semi-chain module can also be called a semi-uniserial module. In [a1] the terms $\Sigma$-uniserial and $\sigma$-uniserial are used for a direct sum of uniserial modules (respectively, a finite direct sum of uniserial modules).


[a1] C. Faith, "Algebra" , II. Ring theory , Springer (1976) pp. Chapt. 25
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Semi-chain module. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article