Kara, Y., Tercan, A., Yaşar, R. (2017). $PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings. Bulletin of the Iranian Mathematical Society, 43(1), 121-129.

Y. Kara; Adnan Tercan; R. Yaşar. "$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings". Bulletin of the Iranian Mathematical Society, 43, 1, 2017, 121-129.

Kara, Y., Tercan, A., Yaşar, R. (2017). '$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings', Bulletin of the Iranian Mathematical Society, 43(1), pp. 121-129.

Kara, Y., Tercan, A., Yaşar, R. $PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings. Bulletin of the Iranian Mathematical Society, 2017; 43(1): 121-129.

$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings

^{1}Hacettepe University, Faculty of Science, Department of Mathematics, 06532, Beytepe, Ankara, Turkey.

^{2}Hacettepe University Department of Mathematics

Receive Date: 05 November 2014,
Revise Date: 20 October 2015,
Accept Date: 20 October 2015

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.

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