Iranian Mathematical Society Title:. P I-extending modules via nontrivial com-plex bundles and Abelian endomorphism rings P I-EXTENDING MODULES VIA NONTRIVIAL COMPLEX BUNDLES AND ABELIAN ENDOMORPHISM RINGS

Author, Kara, A Tercan, R Ya¸sar, Ya¸sar, Y Kara, A Tercan, R Yas¸aryas¸ar
2017 Bull. Iranian Math. Soc   unpublished
A module is said to be P I-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 P I-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 P I-extending property is
more » ... inherited by direct summands. Moreover, we show that under some module theoretical conditions P I-extending modules with Abelian endomorphism rings have indecomposable decompositions. Finally, under suitable hypotheses, we apply our former results to obtain that the finite exchange property implies the full exchange property.