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Matrix Algebras over Strongly Non-Singular Rings
(2014-03-31)
We consider some existing results regarding rings for which the classes of torsion-free and non-singular right modules coincide. Here, a right R-module M is non-singular if xI is nonzero for every nonzero x in M and every ...
Morita-Equivalence Between Strongly Non-Singular Rings and the Structure of the Maximal Ring of Quotients
(2017-07-22)
This dissertation focuses on extending certain notions from Abelian group theory and module theory over integral domains to modules over non-commutative rings. In particular, we investigate generalizations of torsion-freeness ...