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Matrix Algebras over Strongly Non-Singular Rings
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
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 ...