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Article

Příhoda, Pavel
$\operatorname{Add}(U)$ of a uniserial module. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 47 (2006), issue 3, pp. 391-398
MSC: 16D70 | MR 2281002 | Zbl 1106.16006
Keywords:
serial modules; direct sum decomposition
Summary:
A module is called uniserial if it has totally ordered submodules in inclusion. We describe direct summands of $U^{(I)}$ for a uniserial module $U$. It appears that any such a summand is isomorphic to a direct sum of copies of at most two uniserial modules.
References:
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[4] Příhoda P.: On uniserial modules that are not quasi-small. J. Algebra, to appear. MR 2225779
[5] Příhoda P.: A version of the weak Krull-Schmidt theorem for infinite families of uniserial modules. Comm. Algebra, to appear. MR 2224888
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