Author/Authors :
-، - نويسنده Hacettepe University, Faculty of Science, Department of Mathematics, 06532, Beytepe, Ankara, Turkey. Kara, Y. , -، - نويسنده Hacettepe University Department of Mathematics Tercan, Adnan , -، - نويسنده Hacettepe University, Faculty of Science, Department of Mathematics, 06532, Beytepe, Ankara, Turkey. Yaşar, R.
Abstract :
A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper surfaces in projective spaces over complex numbers and obtain results when the $PI$-extending property is inherited by direct summands. Moreover, we show that under some module theoretical conditions $PI$-extending modules with Abelian endomorphism rings have indecomposable decompositions. Finally, we apply our former results, getting that, under suitable hypotheses, the finite exchange property implies the full exchange property.
