Rocky Mountain Journal of Mathematics

On weakly coherent rings

Chahrazade Bakkari and Najib Mahdou

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Abstract

In this paper, we define weakly coherent rings and examine the transfer of this property to homomorphic images, trivial ring extensions, localizations and finite direct products. 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 under localization. Also, we show that the class of weakly coherent rings and the class of strongly $2$-coherent rings are not comparable.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 3 (2014), 743-752.

Dates
First available in Project Euclid: 28 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1411945662

Digital Object Identifier
doi:10.1216/RMJ-2014-44-3-743

Mathematical Reviews number (MathSciNet)
MR3264480

Zentralblatt MATH identifier
1301.13023

Subjects
Primary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 13B05: Galois theory 13A15: Ideals; multiplicative ideal theory 13D05: Homological dimension 13B25: Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]

Keywords
Weakly coherent ring coherent ring homomorphic image trivial ring extension localization direct product

Citation

Bakkari, Chahrazade; Mahdou, Najib. On weakly coherent rings. Rocky Mountain J. Math. 44 (2014), no. 3, 743--752. doi:10.1216/RMJ-2014-44-3-743. https://projecteuclid.org/euclid.rmjm/1411945662


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