# On weakly coherent rings

@article{Bakkari2010OnWC, title={On weakly coherent rings}, author={Chahrazade Bakkari and Najib Mahdou}, journal={Rocky Mountain Journal of Mathematics}, year={2010}, volume={44}, pages={743-752} }

In this paper, we define weakly coherent rings, and examine the transfer of these rings to homomorphic image, trivial ring extension, localization, and direct product. These results provide examples of weakly coherent rings that are not coherent rings. We show that the class of weakly coherent rings is not stable by localization. Also, we show that the class of weakly coherent rings and the class of strongly 2-coherent rings are not comparable.

## One Citation

WEAKLY COHERENT PROPERTY IN AMALGAMATED

- Mathematics
- 2018

called the amalgamation of A and B along J with respect to f (introduced and studied by D’Anna, Finocchiaro, and Fontana in [9, 10]). This constuction is a generalization of the amalgamated…

## References

SHOWING 1-10 OF 18 REFERENCES

On 2-von Neumann Regular Rings

- Mathematics
- 2005

In this article, we consider 2-von Neumann regular rings, that is, rings R with the property that, if F 2 → F 1 → F 0 → E → 0 is an exact sequence of R-modules with F 0, F 1, and F 2 finitely…

Trivial Extensions Defined by Coherent-like Conditions

- Mathematics
- 2004

Abstract This paper investigates coherent-like conditions and related properties that a trivial extension R ≔ A ∝ E might inherit from the ring A for some classes of modules E. It captures previous…

Trivial Extensions of Local Rings and a Conjecture of Costa

- Mathematics
- 2002

This paper partly settles a conjecture of Costa on (n,d)-rings, i.e., rings in which n-presented modules have projective dimension at most d. For this purpose, a theorem studies the transfer of the…

Commutative Coherent Rings

- Mathematics, Physics
- 1989

Preliminaries.- to coherence.- Fundamental concepts.- Ring extensions.- Ring constructions and overrings.- Particular coherent rings.- Polynomial rings.- Coherent algebras.

ON COSTA'S CONJECTURE

- Mathematics
- 2001

Fn ! Fn 1 ! ! F0 ! M ! 0 of R-modules in which each Fi is finitely generated and free. In particular, 0-presented and 1-presented R-modules are finitely generated and finitely presented R-modules…

An Introduction to Homological Algebra

- Mathematics
- 1979

An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext…

Non Commutative Algebra

- Mathematics
- 1994

We have seen (p. 62) how the first non commutative algebras made their appearance in 1843–44, in the work of Hamilton [145 a] and of Grassmann ([134], v. I2). Hamilton, in introducing the…

Parameterizing families of non-noetherian rings

- Mathematics
- 1994

(1994). Parameterizing families of non-noetherian rings. Communications in Algebra: Vol. 22, No. 10, pp. 3997-4011.

Controlling the Zero-Divisors of a Commutative Ring

- Lecture Notes in Pure and Appl. Math., Dekker, 231
- 2003