Advanced SearchSearch Tips
On Strongly Extending Modules
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 2,  2014, pp.237-247
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.2.237
 Title & Authors
On Strongly Extending Modules
Atani, S. Ebrahimi; Khoramdel, M.; Hesari, S. Dolati Pish;
  PDF(new window)
The purpose of this paper is to introduce the concept of strongly extending modules which are particular subclass of the class of extending modules, and study some basic properties of this new class of modules. A module M is called strongly extending if each submodule of M is essential in a fully invariant direct summand of M. In this paper we examine the behavior of the class of strongly extending modules with respect to the preservation of this property in direct summands and direct sums and give some properties of these modules, for instance, strongly summand intersection property and weakly co-Hopfian property. Also such modules are characterized over commutative Dedekind domains.
Extending modules;Strongly extending modules;Strongly Rickart module;
 Cited by
G. F. Birkenmeier, J. K. Park and S. T. Rizvi, Generalized triangular matrix rings and the fully invariant extending property, Rocky Mountain J. Math., 32(2002), 1299-1319. crossref(new window)

G. F. Birkenmeier, J. K. Park and S. T. Rizvi, Modules with fully invariant submodules essential in fully invariant summands. Comm. Algebra, 30(4)(2002), 1833-1852. crossref(new window)

G. F. Birkenmeier, B. J. Muller and S. T. Rizvi, Modules in which every fully invariant submodule is essential in a direct summands. Comm. Algebra, 30(3)(2002), 1395-1415. crossref(new window)

G. F. Birkenmeier, G. Calugareanu, L. Fuchs and H. P. Goeters, The fully invariant extending property for Abelian groups. Comm. Algebra, 29(2)(2001), 673-685. crossref(new window)

N. V. Dung, D. V. Huynh, P. F. Smith, and R. Wisbauer, Extending Modules, Pitman, Research Notes in Mathematics 313. Harlow: Longman (1994).

A. Haghany, M. R. Vedadi, Modules whose injective endomorphisms are essential, J. Algebra, 243(2001), 765-779. crossref(new window)

A. Harmanci, P. F. Smith, Finite direct sums of CS modules, Houston J. Math., 19(4)(1993), 523-532.

M. Harada, On modules with extending property, Osaka J. Math 19 (1982), 203-215.

M. Kamal, B. J. Muller, Extending modules over commutative domains, Osaka J. Math., 25(3)(1988), 531-538.

T. Y. Lam, Lectures on Modules and Rings, Springer-Varlag, New York, (1999).

G. Lee, S. T. Rizvi and C. S. Roman, Rickart Modules. Comm in Algebra, 38(2010), 4005-4027. crossref(new window)

Z. Liu, Direct Sums of Extending Modules, Kyungpook Math. J., 43(2003), 157-162.

A. C. Ozcan, A. Harmanci and P. F. Smith, Duo modules. Glasg. Math. J., 48(2006), 533-545. crossref(new window)

S. T. Rizvi, C. S. Roman, Baer and quasi-Baer modules. Comm. Algebra, 32(1)(2004), 103-123. crossref(new window)

S. T. Rizvi, C. S. Roman, On K-nonsingular modules and applications. Comm. Alge-bra, 35(2007), 2960-2982. crossref(new window)