On retractability and its relationships with lattices associated to a ring

Year 2021, Volume: 50 Issue: 4, 1079 - 1093, 06.08.2021

Rodrigo Domínguez-lópez Oscar Alberto Garrido-jıménez , Hugo Alberto Rincon Mejia , Manuel Gerardo Zorrilla-noriega

https://doi.org/10.15672/hujms.799818

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

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