# On Presented Dimensions of Modules and Rings

## Related Articles

- Projective and generating modules over the ring of pseudorational numbers. Tsarev, A. // Mathematical Notes;Sep/Oct2006, Vol. 80 Issue 3/4, p417
The projective, flat, and generating modules over the ring of pseudorational numbers are described. For the projective modules, a complete independent system of invariants is constructed.

- PURE-PROJECTIVE MODULES. GENA PUNINSKI; PHILIPP ROTHMALER // Journal of the London Mathematical Society;Apr2005, Vol. 71 Issue 2, p304
The question is addressed of when all pure-projective modules are direct sums of finitely presented modules. It is proved that this is the case over hereditary noetherian rings. Partial results are obtained for uniserial rings. Some of the methods are model-theoretic, and the techniques...

- A Note on c-Separative Modules. Huanyin Chen // Kyungpook Mathematical Journal;2007, Vol. 47 Issue 3, p357
A right R-module P is c-separative provided that P âŠ• P â‰…c = P âŠ• Q &Arr; P â‰… Q for any right R-module Q. We get, in this paper, two sufficient conditions under which a right module is c-separative. A ring R is a hereditary ring provided that every ideal of R is...

- Gorenstein projective dimensions of complexes. Liu, Zhong; Zhang, Chun // Acta Mathematica Sinica;Jul2011, Vol. 27 Issue 7, p1395
We show that over a right coherent left perfect ring R, a complex C of left R-modules is Gorenstein projective if and only if C is Gorenstein projective in R-Mod for all m âˆˆ â„¤. Basing on this we show that if R is a right coherent left perfect ring then Gpd( C) = sup{Gpd( C)| m âˆˆ...

- Extensions and s-comparability of exchange rings. Chaoling Huang // Turkish Journal of Mathematics;Dec2012, Vol. 36 Issue 4, p544
Let S be a ring extension of R. In this note, for any positive integer s we study s-comparability related to ring extensions. We show that if S is an excellent extension of R, R and S are exchange rings, and R has the n-unperforation property. R satisfies s-comparability if and we only if so...

- Relatively Projection and Quasi-Green Correspondents. Kewei Lü; Jinglong Cao // Southeast Asian Bulletin of Mathematics;2003, Vol. 27 Issue 3, p487
In this paper, we study the relatively projective modules and quasi-Green correspondents, which is a generalization of Green correspondence to some extent.

- Properties of RD-projective and RD-injective modules. Lixin Mao // Turkish Journal of Mathematics;2011, Vol. 35 Issue 2, p187
In this paper, we first study RD-projective and RD-injective modules using, among other things, covers and envelopes. Some new characterizations for them are obtained. Then we introduce the RD-projective and RD-injective dimensions for modules and rings. The relations between the RD-homological...

- Cofiniteness with respect to a Serre subcategory. Hajikarimi, A. // Mathematical Notes;Feb2011, Vol. 89 Issue 1/2, p121
Let Î¦ be a system of ideals in a commutative Noetherian ring R, and let [InlineMediaObject not available: see fulltext.] be a Serre subcategory of R-modules. We set . Suppose that a is an ideal of R, and M and N are two R-modules such that M is finitely generated and N âˆˆ...

- On Nonnil-Noetherian Rings. Yang, X. Y.; Liu, Z. K. // Southeast Asian Bulletin of Mathematics;2009, Vol. 33 Issue 6, p1215
It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we characterize Nonnil-Noetherian rings by nonniMnjective modules. If R is a commutative ring, then we prove that R is a Nonnil-Noetherian ring if and only...