On retractability and its relationships with lattices associated to a ring

Authors : Rodrigo DOMÍNGUEZ-LÓPEZ, Oscar Alberto GARRİDO-JIMÉNEZ, Hugo Alberto RİNCON MEJİA, Manuel Gerardo ZORRİLLA-NORİEGA

Pages : 1079-1093

Doi:10.15672/hujms.799818

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Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :The purpose of this work is threefold. First, we explore some relationships between retractability and some lattices of classes of modules. Secondly, we weaken the hypothesis of a result of Ohtake characterizing rings over which all radicals are left exact. In the last section of this work, we introduce a binary relation between modules that produce a Galois connection between the lattice of natural classes and the lattice of conatural classes, and we obtain some results about it.
Keywords : left mod retractable ring, parainjective module, paraprojective module, left semiartinian ring, left max ring, left local ring, left duo ring, left V ring, strongly left mod retractable ring