Generalizations of t-extending modules relative to fully invariant submodules
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The concepts of t-extending and t-Baer for modules are generalized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer properties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.
Abstract
The concepts of t-extending and t-Baer for modules are generalized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer properties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.
참고문헌 (11)
- Sh. Asgari, "T-extending modules and t-Baer modules", Comm. Algebra, 39, pp.1605~1623 (2011)
- G. F. Birkenmeier, "The fully invariant extending property for abelian groups", Comm. Algebra, 29(2), pp.673~685 (2001)
- G. F. Birkenmeier, "Modules in which every fully invariant submodule is essential in a direct summand", Comm. Algebra, 30(3), pp.1395~1415 (2002)
- G. F. Birkenmeier, "Modules with fully invariant submodules essential in fully invariant summands", Comm. Algebra, 30(4), pp.1833~1852 (2002)
- G. F. Birkenmeier, "Generalized triangular matrix rings and the fully invariant extending property", Rocky Mountain J. Math, 32(4), pp.1299~1319 (2002)
- G. F. Birkenmeier, "Modules with FI-extending hulls", Glasg. Math. J, 51(2), pp.347~357 (2009)
- M. A. Kamal, "CS-modules and annihilator conditions", Int. J. Math. Math. Sci, 50, pp.3195~3202 (2003)
- T. Y. Lam, "Lectures on Modules and Rings. Graduate Texts in Mathematics, Vol. 189" (1998), Springer-Verlag
- A. C. Ozcan, "Duo modules", Glasg. Math. J, 3, pp.533~545 (2006)
- S. T. Rizvi, "Baer and quasi-Baer modules", Comm. Algebra, 32(1), pp.103~123 (2004)
- R. Wisbauer, "Ikeda-Nakayama modules", Beitrage Algebra Geom, 43(1), pp.111~119 (2002)