Rocky Mountain Journal of Mathematics

On weakly coherent rings

Chahrazade Bakkari and Najib Mahdou

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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.

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

First available in Project Euclid: 28 September 2014

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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]

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


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.

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