View source for Semi-chain module

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



====Comments====
A chain module is also called a uniserial module; correspondingly, a semi-chain module can also be called a semi-uniserial module. In [[#References|[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).

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  C. Faith,   "Algebra" , '''II. Ring theory''' , Springer  (1976)  pp. Chapt. 25</TD></TR></table>