Strongly rectifiable and S-homogeneous modules

Libuše Tesková

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 5-20
  • ISSN: 1509-9415

Abstract

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In this paper we introduce the class of strongly rectifiable and S-homogeneous modules. We study basic properties of these modules, of their pure and refined submodules, of Hill's modules and we also prove an extension of the second Prüfer's theorem.

How to cite

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Libuše Tesková. "Strongly rectifiable and S-homogeneous modules." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 5-20. <http://eudml.org/doc/287706>.

@article{LibušeTesková2000,
abstract = {In this paper we introduce the class of strongly rectifiable and S-homogeneous modules. We study basic properties of these modules, of their pure and refined submodules, of Hill's modules and we also prove an extension of the second Prüfer's theorem.},
author = {Libuše Tesková},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {strongly rectifiable module; S-homogeneous module; pure submodule; refined submodule; pure composite series; Hill's module; strongly rectifiable modules; -homogeneous modules; pure submodules; refined submodules; pure composition series; Hill modules; uniserial submodules; direct sums},
language = {eng},
number = {1},
pages = {5-20},
title = {Strongly rectifiable and S-homogeneous modules},
url = {http://eudml.org/doc/287706},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Libuše Tesková
TI - Strongly rectifiable and S-homogeneous modules
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 5
EP - 20
AB - In this paper we introduce the class of strongly rectifiable and S-homogeneous modules. We study basic properties of these modules, of their pure and refined submodules, of Hill's modules and we also prove an extension of the second Prüfer's theorem.
LA - eng
KW - strongly rectifiable module; S-homogeneous module; pure submodule; refined submodule; pure composite series; Hill's module; strongly rectifiable modules; -homogeneous modules; pure submodules; refined submodules; pure composition series; Hill modules; uniserial submodules; direct sums
UR - http://eudml.org/doc/287706
ER -

References

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  1. [1] K. Benabdallah, A. Bouanane and S. Singh, On sums of uniserial modules, Rocky Mountain J. Math. 20 (1990), 15-29. Zbl0718.16005
  2. [2] K. Benabdallah and S. Hattab, Modules localement rectifiables et modules rectifiables preprint, Université de Montréal (1985). 
  3. [3] K. Benabdallah and S. Hattab, Rectifiable modules. I, Comment. Math. Univ. St. Paul. 37 (1988), 131-143. Zbl0666.16016
  4. [4] L. Bican, Kulikov's criterion for modules, J. Reine Angew. Math. 288 (1976), 154-159. Zbl0333.16021
  5. [5] L. Bican, The structure of primary modules, Acta Univ. Carolin. Math. Phys. 17 (1976) no. 2, 3-12. Zbl0395.16027
  6. [6] A. Facchini and L. Salce, Uniserial modules, Comm. Algebra 18 (2) (1990), 499-517. Zbl0712.16008
  7. [7] T.S. Shores, Decomposition of finitely generated modules, Proc. Amer. Math. Soc. 30 (1971), 445-450. Zbl0203.05002
  8. [8] T.S. Shores, The structure of Loewy modules, J. Reine Angew. Math. 254 (1972), 204-220. Zbl0235.16024

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