Semihollow-Lifting Modules and Projectivity

Authors

Mukdad Qaess Hussain, College of Education for pure science, Diyala University, Diyala, Iraq.Follow
Anfal Hasan Dheyab, Department of Mathematics, College of Education Basic, Diyala University, Diyala, Iraq.Follow
Rana Aziz - Yousif, Al-mansur University College, Baghdad, Iraq.Follow

Abstract

Throughout this paper, T is a ring with identity and F is a unitary left module over T. This paper study the relation between semihollow-lifting modules and semiprojective covers. proposition 5 shows that If T is semihollow-lifting, then every semilocal T-module has semiprojective cover. Also, give a condition under which a quotient of a semihollow-lifting module having a semiprojective cover. proposition 2 shows that if K is a projective module. K is semihollow-lifting if and only if For every submodule A of K with K/( A) is hollow, then K/( A) has a semiprojective cover.

Keywords

Projective cover, Projective modules, Semihollow lifting modules

Article Type

Article

How to Cite this Article

Hussain, Mukdad Qaess; Dheyab, Anfal Hasan; and Yousif, Rana Aziz - (2022) "Semihollow-Lifting Modules and Projectivity," Baghdad Science Journal: Vol. 19: Iss. 4, Article 1.
DOI: https://doi.org/10.21123/bsj.2022.19.4.0811