%0 Journal Article
%T $PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Kara, Y.
%A Tercan, Adnan
%A Yaşar, R.
%D 2017
%\ 02/22/2017
%V 43
%N 1
%P 121-129
%! $PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings
%K extending module
%K projective invariant
%K tangent bundle
%K exchange property
%R
%X 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.
%U http://bims.iranjournals.ir/article_999_9307a1ce4337ba7bd09adbd5dc888465.pdf