Multiplication modules and related results

Shahabaddin Ebrahimi Atani

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 4, page 407-414
  • ISSN: 0044-8753

Abstract

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Let R be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication R -module (see [8], [12] and [3]).

How to cite

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Ebrahimi Atani, Shahabaddin. "Multiplication modules and related results." Archivum Mathematicum 040.4 (2004): 407-414. <http://eudml.org/doc/249318>.

@article{EbrahimiAtani2004,
abstract = {Let $R$ be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication $R$-module (see [8], [12] and [3]).},
author = {Ebrahimi Atani, Shahabaddin},
journal = {Archivum Mathematicum},
keywords = {multiplication module; secondary module; Ohm’s properties; multiplication module; secondary module; Ohm's properties},
language = {eng},
number = {4},
pages = {407-414},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Multiplication modules and related results},
url = {http://eudml.org/doc/249318},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Ebrahimi Atani, Shahabaddin
TI - Multiplication modules and related results
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 4
SP - 407
EP - 414
AB - Let $R$ be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication $R$-module (see [8], [12] and [3]).
LA - eng
KW - multiplication module; secondary module; Ohm’s properties; multiplication module; secondary module; Ohm's properties
UR - http://eudml.org/doc/249318
ER -

References

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  8. Gilmer R., Grams A., The equality ( A ∩ B ) n = A n ∩ B n for ideals, Canad. J. Math. 24 (1972), 792–798. (1972) MR0308109
  9. Low G. H., Smith P. F., Multiplication modules and ideals, Comm. Algebra 18 (1990), 4353–4375. (1990) Zbl0737.13001MR1084452
  10. Lu, C-P., Spectra of modules, Comm. Algebra 23 (10) (1995), 3741–3752. (1995) MR1348262
  11. Macdonald I. G., Secondary representation of modules over commutative rings, Symposia Matematica 11 (Istituto Nazionale di alta Matematica, Roma, (1973), 23–43. (1973) MR0342506
  12. Naoum A. G., The Ohm type properties for finitely generated multiplication ideals, Period. Math. Hungar. 18 (1987), 287–293. (1987) Zbl0628.13002MR0902516
  13. Smith P. F., Some remarks on multiplication module, Arch. Math. 50 (1988), 223–235. (1988) MR0933916
  14. Schenzel S., Asymptotic attached prime ideals to injective modules, Comm. Algebra 20 (2) (1992), 583–590. (1992) MR1146316

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