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On Generalizations of Extending Modules
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  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 3,  2009, pp.557-562
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.3.557
 Title & Authors
On Generalizations of Extending Modules
Karabacak, Fatih;
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A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about and SIP-modules.
SIP-extending modules;summand intersection property;extending modules;
 Cited by
CS-Rickart modules, Lobachevskii Journal of Mathematics, 2014, 35, 4, 317  crossref(new windwow)
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, 1974.

D. M. Arnold and J. Hausen, A characterization of modules with the summand intersection property, Comm. Algebra, 18(1990), 519-528. crossref(new window)

G. F. Birkenmeier, F. Karabacak and A. Tercan, When is the SIP (SSP) property inherited by free modules, Acta Math. Hungar., 112(2006), 103-106. crossref(new window)

G. F. Birkenmeier, J. Y. Kim and J. K. Park, When is the CS condition hereditary?, Comm. Algebra, 27(1999), 3785-3885. crossref(new window)

N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, Longman, 1990.

J. Hausen, Modules with the summand intersection property, Comm. Algebra, 17(1989), 135-148. crossref(new window)

I. Kaplansky, Infinite Abelian Groups, University of Michigan Press, 1969.

F. Karabacak and A. Tercan, Matrix rings with the summand intersection property, Czech. Math. J., 53(2003), 621-626. crossref(new window)

F. Karabacak and A. Tercan, On modules and matrix rings with SIP-extending, Taiwanese J. Math., 11(2007), 1037-1044.

N. K. Kim and Y. Lee, Armendariz rings and reduced rings, Journal of Algebra, 223(2000), 477-488. crossref(new window)

S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, Cambridge University Press, 1990.

K. Oshiro and S. T. Rizvi, Exchange property of quasi-continuous modules with the finite exchange property, Osaka J. Math., 33(1996), 217-234.

S. T. Rizvi and C. S. Roman, Baer and quasi-baer modules, Comm. Algebra, 32(2004), 103-123. crossref(new window)

P. F. Smith, Modules for which every submodule has a unique closure, Ring Theory (S.Jain and S.T. Rizvi eds.) New Jersey, World Scientific, (1992), 302-317.

P. F. Smith and A. Tercan, Generalizations of CS-modules, Comm. Algebra, 21(1993), 1809-1847. crossref(new window)

P. F. Smith and A. Tercan, Direct summands of modules which satisfy (C11), Algebra Colloq., 11(2004), 231-237.

G. V. Wilson, Modules with the summand intersection property, Comm. Algebra, 14(1986), 21-38. crossref(new window)