On retractability and its relationships with lattices associated to a ring

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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