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arXiv · 1707.02542

Melkersson conditions with respect to a prime ideal

Takeshi Yoshizawa
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Abstract

Aghapournahr and Melkersson introduced the notion of Melkersson condition on a Serre subcategory of the module category over a commutative noetherian ring. This paper investigates the structure of set of prime ideals satisfying a Melkersson condition on a Serre subcategory. We try to calculate members of a set of these prime ideals for a subcategory consisting of extension modules in two given Serre subcategories of the module category. Meanwhile, we classify the structure of set of prime ideals satisfying a Melkersson condition over a 0-dimensional ring, a 1-dimensional local ring, and a 2-dimensional local domain.

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Takeshi Yoshizawa. 2017-07-09. Melkersson conditions with respect to a prime ideal. https://arxiv.org/abs/1707.02542

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