Projective modules and prime submodules

Mustafa Alkan; Yücel Tiraş

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 601-611
  • ISSN: 0011-4642

Abstract

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In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics: (i) The existence of prime submodules in some cases, (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property.

How to cite

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Alkan, Mustafa, and Tiraş, Yücel. "Projective modules and prime submodules." Czechoslovak Mathematical Journal 56.2 (2006): 601-611. <http://eudml.org/doc/31052>.

@article{Alkan2006,
abstract = {In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics: (i) The existence of prime submodules in some cases, (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property.},
author = {Alkan, Mustafa, Tiraş, Yücel},
journal = {Czechoslovak Mathematical Journal},
keywords = {prime submodule; primary submodule; $\{\mathcal \{S\}\}$-closed subsets; the radical formula; primary submodule; the radical formula},
language = {eng},
number = {2},
pages = {601-611},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Projective modules and prime submodules},
url = {http://eudml.org/doc/31052},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Alkan, Mustafa
AU - Tiraş, Yücel
TI - Projective modules and prime submodules
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 601
EP - 611
AB - In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics: (i) The existence of prime submodules in some cases, (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property.
LA - eng
KW - prime submodule; primary submodule; ${\mathcal {S}}$-closed subsets; the radical formula; primary submodule; the radical formula
UR - http://eudml.org/doc/31052
ER -

References

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