Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T08:34:23.224Z Has data issue: false hasContentIssue false

Quasi-copure Submodules

Published online by Cambridge University Press:  20 November 2018

Saeed Rajaee*
Affiliation:
Department of Mathematics, Faculty of Mathematics, Payame Noor University (PNU), P.O. Box, 19395-3697, Tehran, Iran e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

All rings are commutative with identity, and all modules are unital. In this paper we introduce the concept of a quasi-copure submodule of a multiplication $R$-module $M$ and will give some results about it. We give some properties of the tensor product of finitely generated faithful multiplication modules.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2016

References

[1] Ali, M. M., 1/2 cancellation modules and homogeneous idealization. IL Comm. Algebra 36(2008), 38423864. http://dx.doi.Org/10.1080/00927870802160826 Google Scholar
[2] Ali, M. M., Multiplication modules and tensor product. Beitrâge Algebra Geom. 47(2006), no. 2, 305327.Google Scholar
[3] Ali, M. M., Some remarks on Multiplication and flat modules. J. Commut. Algebra 4(2012), no. 1, 127. http://dx.doi.Org/10.121 6/JCA-2O12-4-1-1 Google Scholar
[4] Ali, M. M., Some remarks on multiplication and projective modules. IL Comm. Algebra 41(2013), 195214. http://dx.doi.Org/10.1080/00927872.2011.628724 Google Scholar
[5] Ansari-Toroghy, H. and Farshadifar, F.. On comultiplication modules. Korean Ann Math. 25(2008), no. 1-2, 5766.Google Scholar
[6] Barnard, A. D., Multiplication modules. J. Algebra 71(1981), 174178. http://dx.doi.Org/10.101 6/0021-8693(81)90112-5 Google Scholar
[7] El-Bast, Z. A. and Smith, P. F., Multiplication modules. Comm. Algebra 16(1988), 755779. http://dx.doi.Org/10.1080/00927878808823601 Google Scholar
[8] Faith, C., Algebra I: Rings, modules, and categories. Grundlehren der Mathematischen Wissenschaften, 190, Springer-Verlag, Berlin-New York, 1981.Google Scholar
[9] McCasland, R. L. and Moore, M. E., On radicals of finitely generated modules. Canad. Math. Bull. 29(1986), no. 1, 3739. http://dx.doi.Org/10.4153/CMB-1986-006-7 Google Scholar
[10] Naoum, A. G. and Al-Alwan, F. H., Dedekind modules. Comm. Algebra 24(1996), no. 2. 397412. http://dx.doi.Org/10.1080/00927879608825576 Google Scholar
[11] Smith, P. F., Some remarks on multiplication modules. Arch. Math. (Basel) 50(1988), 223235. http://dx.doi.Org/10.1007/BF01187738 Google Scholar