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Almahdi, Fuad Ali Ahmed
- 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.References
- D. Bennis and N. Mahdou, On n-perfect rings and cotorsion dimension, J. Algebra Appl., 8 (2009) 181–190.
- L. Bican, E. Bashir and E. E. Enochs, All modules have flat covers, Bull. London Math. Soc., 33 (2001) 385–390.
- N. Bourbaki, Algebre commutative: chapitre 10, Springer-Verlag, Berlin (2007).
- N. Ding and L. Mao, The cotorsion dimension of modules and rings, in: Abelian Groups, Modules and Homological Algebra, in: Lect. Notes Pure Appl. Math., Vol. 249, (Chapman and Hall, 2006) 217–243.
- S. El Baghdadi and S. Gabelli, Ring-theoretic properties of PVMDs, Comm. Algebra, 35 (2007) 1607–1625.
- E. E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math., 39 (1981) 189–209.
- E. E. Enochs, Flat covers and flat cotorsion modules, Proc. Amer. Math. Soc., 92 (1984) 179–184.
- S. Glaz, Commutative coherent rings, Springer, Berlin (1989).
- M. Griffin, Some results on v-multiplication rings, Canad. J. Math., 19 (1967) 710–722.
- E. Houston, S. Kabbaj and A. Mimouni, Star-reductions of ideals and Prufer v-multiplication domains, J. Commut. Algebra (To appear).
- B. G. Kang, Some questions about Prufer v-multiplication domains, Comm. Algebra, 17 (1989) 553–564.
- H. Kim and F.Wang, On LCM-stable modules, J. Algebra Appl., 13 (2014) 1350133, 18 pp.
- N. Mahdou, On Costa’s conjecture, Comm. Algebra, 29(7) (2001) 2775–2785.
- L. Mao and N. Ding, Notes on cotorsion modules, Comm. Algebra, 33 (2005) 349–360.
- A. Mimouni, Integral domains in which each ideal is a w-ideal, Comm. Algebra, 33 (2005) 1345–1355.
- W. K. Nicholson and M. F. Yousif, Quasi-Frobenius Rings, Cambridge University Press, New York (2003).
- J. Rotman, An introduction to homological algebra, Springer, New York (2008).
- W. V. Vasconcelos, The local rings of global dimension two, Proc. Amer. Math. Soc., 35 (1972) 381–386.
- F. Wang, On w-projective modules and w-flat modules, Algebra Colloq., 4 (1997) 111–120.
- F. Wang, Finitely presented type modules and w-coherent rings, J. Sichuan Normal Univ., 33 (2010) 1–9.
- F. Wang and H. Kim, w-Injective modules and w-semi-hereditary rings, J. Korean Math. Soc., 51 (2014) 509–525.
- F. Wang and H. Kim, Two generalizations of projective modules and their applications, J. Pure Appl. Algebra, 219 (2015) 2099–2123.
- F. Wang and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra, 25 (1997) 1285–1306.
- F. Wang and L. Qiao, The w-weak global dimension of commutative rings, Bull. Korean Math. Soc., 52 (2015) 1327–1338.
- F. Wang and J. Zhang, Injective modules over w-Noetherian rings, Acta Math. Sin., 53 (2010) 1119-1130. (in Chinese)
- J. Xu, Flat covers of modules, 1st ed., Springer, Berlin (1996).
- H. Yin, F.Wang, X. Zhu and Y. Chen, w-Modules over commutative rings, J. Korean Math. Soc., 48 (2011) 207–222.
- S. Q. Zhao, F. Wang and H. L. Chen, Flat modules over a commutative ring are w-modules, J. Sichuan Normal Univ., 35 (2012) 364–366. (in Chinese)