QTAG torsionfree modules

Ladislav Bican; Blas Torrecillas

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 1, page 1-20
  • ISSN: 0010-2628

Abstract

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The structure theory of abelian p -groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated p -group is a direct sum of cyclics. Given a hereditary torsion theory on the category R -Mod of unitary left R -modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This paper continues in our previous investigations of the structural properties of such modules.

How to cite

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Bican, Ladislav, and Torrecillas, Blas. "QTAG torsionfree modules." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 1-20. <http://eudml.org/doc/247354>.

@article{Bican1992,
abstract = {The structure theory of abelian $p$-groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated $p$-group is a direct sum of cyclics. Given a hereditary torsion theory on the category $R$-Mod of unitary left $R$-modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This paper continues in our previous investigations of the structural properties of such modules.},
author = {Bican, Ladislav, Torrecillas, Blas},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {torsion theory; torsionfree module; $\sigma $-QTAG-module; kernel of purity; center of purity; hereditary torsion theory; -finitely generated submodule; direct sum of -uniserial modules; -QTAG-modules; decompositions; -purity; -neatness},
language = {eng},
number = {1},
pages = {1-20},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {QTAG torsionfree modules},
url = {http://eudml.org/doc/247354},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Bican, Ladislav
AU - Torrecillas, Blas
TI - QTAG torsionfree modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 1
SP - 1
EP - 20
AB - The structure theory of abelian $p$-groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated $p$-group is a direct sum of cyclics. Given a hereditary torsion theory on the category $R$-Mod of unitary left $R$-modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This paper continues in our previous investigations of the structural properties of such modules.
LA - eng
KW - torsion theory; torsionfree module; $\sigma $-QTAG-module; kernel of purity; center of purity; hereditary torsion theory; -finitely generated submodule; direct sum of -uniserial modules; -QTAG-modules; decompositions; -purity; -neatness
UR - http://eudml.org/doc/247354
ER -

References

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  1. Albu T., Nastasescu C., Relative finiteness in module theory, Pure and Appl. Math. 84, Marcel Dekker, New York, 1984. Zbl0556.16001MR0749933
  2. Bican L., Kulikov's criterion for modules, J. Reine Angew. Math. 288 (1976), 154-159. (1976) Zbl0333.16021MR0422320
  3. Bican L., The structure of primary modules, Acta Math. Universitatis Carolinae 17 (1976), 3-12. (1976) Zbl0395.16027MR0435119
  4. Bican L., Kepka T., Němec P., Rings, Modules and Preradicals, Marcel Dekker, New York, 1982. MR0655412
  5. Bican L., Torrecillas B., A general Kulikov's theorem, Comm. in Algebra 19 (1990), 2453-2486. (1990) MR1125182
  6. Bican L., Torrecillas B., A relative Ulm's theorem, to appear in Rivista Mat. Pura Appl. Zbl0779.16013
  7. Golan J.S., Torsion Theories, Pitman Monographs and Surveys in Pure and Appl. Math., Longman Scientific Publishing, London, 1986. Zbl0695.16021MR0880019
  8. Mehran H., Singh S., On σ -pure submodules of QTAG-modules, Arch. Math. 46 (1986), 501-510. (1986) Zbl0596.16021MR0849855
  9. Singh S., Modules over H.N.P. rings, Can. J. Mat. XXVII (1975), 867-883. (1975) MR0389958
  10. Singh S., Some decompositions theorems in abelian groups and their generalizations, In: Ring Theory: Proc. of Ohio University Conf., Lecture Notes in Pure and Applied Math., Marcel Dekker 25 (1986), 183-189. MR0435146
  11. Singh S., Abelian groups like modules, Acta Math. Hungarica 50 (1987), 85-97. (1987) Zbl0628.16014MR0893248
  12. Stenström B., Rings of Quotients, Springer, Berlin, 1975. MR0389953
  13. Teply M.L., Modules semicocritical with respect to a torsion theory and their applications, Israel J. Math. 54 (1986), 181-200. (1986) Zbl0603.16022MR0852477
  14. Torrecillas B., On Kulikov's theorem, Comm. in Algebra 14 (1986), 1091-1110. (1986) Zbl0592.16017MR0837272
  15. Torrecillas B., Height relative to a torsion theory, Ring theory (Antwerp 1985), Lecture Notes in Math. 1197, Springer, Berlin, 1986. Zbl0589.16021MR0859395
  16. Torrecillas B., Neat submodules by relative height, Comm. in Algebra 17 (1989), 2309-2324. (1989) Zbl0683.16023MR1016867

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