Title:
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CF-modules over commutative rings (English) |
Author:
|
Najim, Ahmed |
Author:
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Charkani, Mohammed Elhassani |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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59 |
Issue:
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1 |
Year:
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2018 |
Pages:
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25-34 |
Summary lang:
|
English |
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Category:
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math |
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Summary:
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Let $R$ be a commutative ring with unit. We give some criterions for determining when a direct sum of two CF-modules over $R$ is a CF-module. When $R$ is local, we characterize the CF-modules over $R$ whose tensor product is a CF-module. (English) |
Keyword:
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CF-couple |
Keyword:
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CF-module |
Keyword:
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commutative ring |
Keyword:
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local ring |
MSC:
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13C05 |
idZBL:
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Zbl 06890394 |
idMR:
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MR3783806 |
DOI:
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10.14712/1213-7243.2015.236 |
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Date available:
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2018-04-17T13:41:12Z |
Last updated:
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2020-04-06 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/147176 |
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Reference:
|
[1] Auslander M., Buchsbaum D. A.: Invariant factors and two criteria for projectivity of modules.Trans. Amer. Math. Soc. 104 (1962), 516–522. 10.1090/S0002-9947-1962-0157987-5 |
Reference:
|
[2] Behboodi M., Ghorbani A., Moradzadeh-Dehkordi A.: Commutative Noetherian local rings whose ideals are direct sums of cyclic modules.J. Algebra 345 (2011), 257–265. 10.1016/j.jalgebra.2011.08.017 |
Reference:
|
[3] Brown William C.: Matrices over Commutative Rings.Marcel Decker Inc., New York, 1993. |
Reference:
|
[4] Charkani M. E., Akharraz I.: Fitting ideals and cyclic decomposition of finitely generated modules.Arab. J. Sci. Eng. Sect. C (2000), 151–156. |
Reference:
|
[5] Cohen I. S., Kaplansky I.: Rings for which every module is a direct sum of cyclic modules.Math. Z. 54 (1951), 97–101. 10.1007/BF01179851 |
Reference:
|
[6] Griffith P.: On the decomposition of modules and generalized left uniserial rings.Math. Ann. 184 (1970), 300–308. 10.1007/BF01350858 |
Reference:
|
[7] Klingler L., Levy L. S.: Representation type of commutative Noetherian rings. I. Local wildness.Pacific J. Math. 200 (2001), no. 2, 345–386. 10.2140/pjm.2001.200.345 |
Reference:
|
[8] Köthe G.: Verallgemeinerte abelsche gruppen mit hyperkomplexen operatorenring.Math. Z. 39 (1935), 31–44. 10.1007/BF01201343 |
Reference:
|
[9] Levy L. S.: Modules over Dedekind-like rings.J. Algebra 93 (1985), 1–116. 10.1016/0021-8693(85)90176-0 |
Reference:
|
[10] Shores T. S., Wiegand R.: Decomposition of modules and matrices.Bull. Amer. Math. Soc. 79 (1973), 1277–1280. 10.1090/S0002-9904-1973-13414-7 |
Reference:
|
[11] Shores T. S., Wiegand R.: Rings whose finitely generated modules are direct sums of cyclics.J. Algebra 32 (1974), 152–172. 10.1016/0021-8693(74)90178-1 |
Reference:
|
[12] Steinitz E.: Rechteckige Systeme und Moduln in Algebraischen Zahlköppern I.Math. Ann. 71 (1911), 328–354 (German). 10.1007/BF01456849 |
Reference:
|
[13] Steinitz E.: Rechteckige Systeme und Moduln in Algebraischen Zahlköppern II.Math. Ann. 72 (1912), 297–345 (German). 10.1007/BF01456721 |
Reference:
|
[14] Warfield R. B. Jr.: A Krull-Schmidt theorem for infinite sums of modules.Proc. Amer. Math. Soc. 22 (1969), 460–465. 10.1090/S0002-9939-1969-0242886-2 |
Reference:
|
[15] Warfield R. B. Jr.: Rings whose modules have nice decompositions.Math. Z. 125 (1972), 187–192. 10.1007/BF01110928 |
Reference:
|
[16] Weintraub S. H.: Representation Theory of Finite Groups: Algebras and Arithmetic.Graduate Studies in Mathematics, 59, American Mathematical Society, Providence, RI, 2003. 10.1090/gsm/059 |
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