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Discussiones Mathematicae General Algebra and Applications 20(1) (2000) 5-20
DOI: https://doi.org/10.7151/dmgaa.1001

STRONGLY RECTIFIABLE AND S-HOMOGENEOUS MODULES

Libuse Tesková

Department of Mathematics Faculty of Applied Sciences
University of West Bohemia
Univerzitní 22, Cz-30614 Pilsen, Czech Republic

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.

Keywords: strongly rectifiable module, S-homogeneous module, pure submodule, refined submodule, pure composite series, Hill's module.

1991 Mathematics Subject Classifications: 16D80, 16D70, 13C13.

References

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

Received 22 September 1997
Revised 28 July 1998