开始从未
发表于 2025-3-23 11:50:56
Unique factorization of m-completions,Let . be an integral domain. We say that . is . (or a Unique Factorization Domain) if every element . ∈ . ≠ 0 and non-unit, has an essentially unique decomposition in irreducible factors. Here “essentially” means “up to unit factors and permutations of the factors”.
混杂人
发表于 2025-3-23 17:39:14
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CLAIM
发表于 2025-3-23 19:03:06
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addition
发表于 2025-3-23 22:25:19
Analytic reducedness,In this section we shall give some sufficient conditions for the reducedness of ĉ-adic completions which are related to the radical of the completion of an ideal. ..
缩减了
发表于 2025-3-24 05:48:40
Normality of m-completions,Let . a ring and . a subring of .. An element . ∈. is said to be . over . if there are .,..., . ∈. such that . + ··· + . + . . (. > 0). The ring . is said to be . if every element of . which is integral over . is an element of .. Finally a domain . is said to be . if . is integrally closed in its quotient field.
Injunction
发表于 2025-3-24 06:47:05
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多节
发表于 2025-3-24 12:42:52
Completions of filtered groups, rings and modules. Applications to m-adic topologies,.. It is clear that .(.) = ∞ if and only if . (lemma 1.1). The mapping allows us to define a . in .: let . be the mapping defined by .(.) = . (we agree that . = 0). Then it is easy to see that . and that . defines in . the topology induced by the filtration (.).
艺术
发表于 2025-3-24 17:15:10
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Phagocytes
发表于 2025-3-24 22:25:02
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光滑
发表于 2025-3-25 02:08:18
Silvio Greco,Paolo Salmonhey have wherein they have lavished out their words freely hath been so long, that they know we cannot catch hold of them to pull them out and they think that we will not write to reprove their lying lips.”. Two decades later, Constantia Munda also wrote scornfully of men, “And Printing, that was in