Add ( U ) of a uniserial module

Pavel Příhoda

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 391-398
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Příhoda, Pavel. "$\operatorname{Add}(U)$ of a uniserial module." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 391-398. <http://eudml.org/doc/249841>.

@article{Příhoda2006,
abstract = {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.},
author = {Příhoda, Pavel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {serial modules; direct sum decomposition; uniserial modules; direct sum decompositions; direct summands},
language = {eng},
number = {3},
pages = {391-398},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\operatorname\{Add\}(U)$ of a uniserial module},
url = {http://eudml.org/doc/249841},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Příhoda, Pavel
TI - $\operatorname{Add}(U)$ of a uniserial module
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 391
EP - 398
AB - 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.
LA - eng
KW - serial modules; direct sum decomposition; uniserial modules; direct sum decompositions; direct summands
UR - http://eudml.org/doc/249841
ER -

References

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  1. Bass H., Big projective modules are free, Illinois J. Math. 7 (1963), 24-31. (1963) Zbl0115.26003MR0143789
  2. Dung N.V., Facchini A., Direct sum decompositions of serial modules, J. Pure Appl. Algebra 133 (1998), 93-106. (1998) MR1653699
  3. Facchini A., Module Theory; Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules, Birkhäuser, Basel, 1998. Zbl0930.16001MR1634015
  4. Příhoda P., On uniserial modules that are not quasi-small, J. Algebra, to appear. MR2225779
  5. Příhoda P., A version of the weak Krull-Schmidt theorem for infinite families of uniserial modules, Comm. Algebra, to appear. MR2224888

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