We show that \\mathcal{PGF} = \\mathcal{DP} \\mathcal{PGF} = \\mathcal{DP} if and only if every Ding projective module is Gorenstein flat. This is the case if the ring R R is coherent for example. We include an example to show that the coherence is a sufficient, but not a...
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Also, it is given a condition to verify certain relation between GC -projectives and GC -flats. Indeed, it is shown that every GC -projective module is GC -flat if and only if for every C -injective module I , the character module is in ....
TheyprovedthateveryGorensteinprojective(resp.Gorensteininjective,Gorensteinflat)moduleis adirectsummandofastronglyGorensteinprojective(resp.stronglyGorensteininjective,strongly Gorensteinflat)module.Inthispaper,wecontinuethestudyofstronglyGorensteinprojective,injec- ...
Theorem. A module is Gorenstein projective (resp., injective) if, and only if, it is a direct summand of a strongly Gorenstein projective (resp., injective) module. Every flat module is a direct summand of a strongly Gorenstein flat module. Over Noetherian rings the Gorenstein projective...
Let R be a ring, n a fixed nonnegative integer and F n the class of all left R-modules of flat dimension at most n. A left R-module M is called n-copure projective if Ext 1 R (M,F) = 0 for any F∈ F n . Some examples are given to show that n-copure projective modules...
The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the behavior of the objects of cocycles in acyclic complexes. It is known that any flat Proj-periodic module is projective, any fp-injective Inj-periodic module is injective, and any Cot-periodic module is cotorsion...
On w-projective modules and w-flat modules A torsion-free module M over a domain r is called w-projective if M_w is of finite type and M_P is free for any maximal w-ideal P of R. In this paper, we s... F Wang - 《Algebra Colloquium》 被引量: 85发表: 1997年 A note on ...
(2) The quotient field Q of an integral domain R is a quasi-projective R-module if and only if every proper submodule of Q is complete in its R -topology. (3) Integral domains all of whose ideals are quasi-projective are exactly the almost maximal Prufer domains.; The second part of...
Let P~ P (~)(n) and N0 (~) (n) be complete subcategories of the category of right ~modules mod 锟 9 whose objects are respectively projective modules p0, p, and flat modules E ~ where the modules p0, p, and ~0 are generated by no more than n elements and the module ~0 is ...