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Assaad, Refat Abdelmawla Khaled
- On the Right Orthogonal Complement of the Class of ω-Flat Modules
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1 Department of Mathematics, Faculty of Science, King Khalid University, P.O.Box 9004, Abha, SA
2 Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Box 11201, Zitoune, MA
1 Department of Mathematics, Faculty of Science, King Khalid University, P.O.Box 9004, Abha, SA
2 Department of Mathematics, Faculty of Science, University Moulay Ismail Meknes, Box 11201, Zitoune, MA
Source
Journal of the Ramanujan Mathematical Society, Vol 33, No 2 (2018), Pagination: 159-175Abstract
Let R be a commutative ring. An R-module M is said to be ω-flat if TorR1 (M, N) is a GV-torsion R-module for all R-modules N. In this paper, we study the flat and projective dimensions of ω-flat modules. To do so, we study the elements of the right orthogonal complement of the class of all ω-flat modules, called ω-cotorsion modules, and we introduce and characterize the ω-cotorsion dimension for modules and rings. The relations between the ω-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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