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Rings with quasi-projective left ideals

Profile image of Surender JainSurender Jain

Pacific Journal of Mathematics

Abstract
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This paper explores the structural properties of perfect left quasi-projective (qp) rings, establishing that all left hereditary rings are included in the class of left qp-rings. It examines the distinctions between commutative principal ideal artinian rings and qp-rings, as well as exploring the relationship between local rings and quasi-projective modules. Key theorems related to the isomorphism of left ideals and the conditions under which a local perfect ring qualifies as a left qp-ring are presented, alongside several lemmas supporting these findings. The results indicate that the properties of quasi-projective modules diverge significantly in the context of perfect rings, highlighting the intricate structures within ring theory.

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