# Modules whose direct summands are FI-extending

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Balkan Campus‎, ‎Trakya University‎, ‎22030 Edirne‎, ‎Turkey.

2 Department of Mathematics‎, ‎Yunus Emre Campus‎, ‎Education Faculty‎, ‎Anadolu University‎, ‎26470 Eskisehir‎, ‎Turkey.

Abstract

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?

Keywords

Main Subjects

### References

G.F. Birkenmeier, B.J. Muller and S.T. Rizvi, Modules in which every fully invariant submodule is essential in a direct summand, Comm. Algebra 30 (2002), no. 3, 1395--1415.

G.F. Birkenmeier, J.K. Park and S.T. Rizvi, Modules with fully invariant submodules essential in fully invariant summands, Comm. Algebra 30 (2002), no. 4, 1833-1852.

N.V. Dung, D.V. Huynh, P.F. Smith and R. Wisbauer, Extending Modules, Pitman Research Notes in Math. Ser. 313, Longman, Harlow, 1994.

F. Karabacak and A. Tercan, On modules and matrix rings with SIP-extending, Taiwanese J. Math. 11 (2007), no. 4, 1037--1044.

P.F. Smith and A. Tercan, Direct summands of modules which satisfy (C11), Algebra Colloq. 11 (2004), no. 2, 231--237.

B. Stenstrom, Rings of Quotients, Springer-Verlag, New York, 1975.

X. Wang and J. Chen, On FI-extending rings and modules, Northeast. Math. J. 24 (2008), no. 1, 77--84.

### History

• Receive Date: 20 July 2016
• Revise Date: 16 January 2017
• Accept Date: 20 January 2017