International Journal of Science, Engineering and TechnologyAuthors: Dr. Sumit Kumar Dekate
Abstract: This paper is extension of my work in my previous paper titled “EXACT MODULES UNDER CHANGE OF RINGS’’ and “GENERALIZATION OF EXACT MODULES UNDER CHANGE OF RINGS” which studies the preservation of exactness of modules under change of rings. The principal results concern surjective ring homomorphisms and the transfer of exactness between module structures induced by such homomorphisms. The paper also records a converse-type result, introduces weakly exact modules, proves a criterion for balanced bimodules, and gives a finite-length criterion involving direct powers M^((n)) .To make the results more transparent for readers, explicit examples are included after the principal results. The present version replaces the earlier illustrations by new examples involving quotient rings, polynomial rings, finite fields, triangular matrix rings, and finite-dimensional modules.
