相持不下
发表于 2025-3-21 17:47:47
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correspondent
发表于 2025-3-21 22:36:26
Affine Algebraic Varieties varieties. In addition, we explore the properties of these varieties and ideals by using the theory of ideals developed so far. Furthermore, we provide a proof of the Hilbert Nullstellensatz, which establishes a fundamental relation between geometry and algebra. We then apply this theorem, along wi
我不重要
发表于 2025-3-22 02:28:07
Localizationring ., or, in greater generality, the construction of the field of fractions of a domain. We will define fractions using as denominators elements of a chosen subset of the ring. We will see that, when we choose the denominators in the complement of a prime ideal, this construction produces a local
vasospasm
发表于 2025-3-22 05:34:39
Noetherian and Artinian Rings. Primary Decomposition finitely generated and can be decomposed as a finite intersection of primary ideals. Additionally, we prove that . is Noetherian if and only if . is Noetherian, and that . is Artinian if and only if, up to isomorphism, it is a finite direct sum of local Artinian rings. This result generalizes what
cauda-equina
发表于 2025-3-22 12:00:51
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Bereavement
发表于 2025-3-22 13:01:42
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Bereavement
发表于 2025-3-22 20:17:26
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必死
发表于 2025-3-23 00:57:25
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故意
发表于 2025-3-23 03:28:19
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向外
发表于 2025-3-23 08:01:50
Localizationa chosen subset of the ring. We will see that, when we choose the denominators in the complement of a prime ideal, this construction produces a local ring whose maximal ideal is the extension of that prime with respect to a canonical homomorphism.