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- W2013497871 abstract "Dans ce document, notre objectif est de revisiter quelques résultats classiques de base sur la dimension de Krull des anneaux commutatifs N -gradués en utilisant la notion récente d'idéaux et de monoïdes bords. Après avoir rappelé le lien entre la dimension de Krull (Kdim) et les idéaux et monoïdes bords, nous avons caractérisé la dimension graduée (dimgr) dans le même esprit. L'objectif principal étant de comparer dimgr A , Kdim A et Kdim ( 1 + A + ) − 1 A , où A désigne un anneau gradué (noethérien ou pas), nous établissons différentes propriétés des idéaux bords, notamment des inclusions d'idéaux bords d'où découlent des relations dimensionnelles. In this paper, we investigate some basic classical results on the Krull dimension of N -graded commutative rings by using the concept of iterated boundary ideals and iterated boundary monoids. After having pointed out the link between the Krull dimension (Kdim) and the boundary ideals and monoids, we characterize in the same way the graded dimension (dimgr). The main goal is to compare dimgr A , Kdim A and Kdim ( 1 + A + ) − 1 A , where A is a graded ring (noetherian or not). To do this, we establish various properties using the boundary ideals, in particular some typical boundary ideals inclusions." @default.
- W2013497871 created "2016-06-24" @default.
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- W2013497871 date "2010-11-01" @default.
- W2013497871 modified "2023-09-24" @default.
- W2013497871 title "Sur les dimensions des anneaux gradués" @default.
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- W2013497871 doi "https://doi.org/10.1016/j.jalgebra.2010.06.031" @default.
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