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Journal of the Ramanujan Mathematical Society

Volume 33, Issue 2, June 2018  pp. 159–175.

On the right orthogonal complement of the class of w-flat modules

Authors:  Fuad Ali Ahmed Almahdi, Mohammed Tamekkante and Refat Abdelmawla Khaled Assaad
Author institution:Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia

Summary:  Let R be a commutative ring. An R-module M is said to be w-flat if Tor R1 (M,N) is a GV-torsion R-module for all R-modules~N. In~this paper, we study the flat and projective dimensions of w-flat modules. To do so, we study the elements of the right orthogonal complement of the class of all w-flat modules, called w-cotorsion modules, and we introduce and characterize the w-cotorsion dimension~for modules and rings. The relations between the w-cotorsion dimension and other dimensions are discussed, and many illustrative examples are given. As applications, we give a new homological characterizations of PvMDs and a new upper bound on the global dimension of rings.

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