Let denote an extension of commutative rings with identity, I be a nonzero proper ideal of D, Γ mean a nonzero torsion-free additive grading monoid with and . Let be the semigroup ring of Γ over E, and the coefficients of nonconstant terms of f belong to I}. In this paper, we give some conditions for the rings (resp., domains) and to be Noetherian (resp., to satisfy the ascending chain condition on principal ideals).
Soient une extension dʼanneaux commutatifs unitaires, I un idéal non nul et propre de D et Γ un monoïde commutatif simplifiable sans torsion non trivial tel que et . Soient lʼanneau semi-groupe de Γ sur E, et les coefficients des termes non-constants de f appartiennent à I}. Dans cet article, nous donnons certaines conditions pour que les anneaux (resp., domaines) et soient Noethériens (resp., satisfassent la condition de chaîne ascendante sur les idéaux principaux).
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Jung Wook Lim 1; Dong Yeol Oh 2
@article{CRMATH_2012__350_13-14_655_0, author = {Jung Wook Lim and Dong Yeol Oh}, title = {Chain conditions in special pullbacks}, journal = {Comptes Rendus. Math\'ematique}, pages = {655--659}, publisher = {Elsevier}, volume = {350}, number = {13-14}, year = {2012}, doi = {10.1016/j.crma.2012.07.003}, language = {en}, }
Jung Wook Lim; Dong Yeol Oh. Chain conditions in special pullbacks. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 655-659. doi : 10.1016/j.crma.2012.07.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.003/
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