Last Updated:2025/12/04
Sentence

主イデアル整域上の任意の自由加群は、その環の直和(複数の同型な因子)に同型である。

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Every free module over a principal ideal domain is isomorphic to a direct sum of copies of the ring.

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Every free module over a principal ideal domain is isomorphic to a direct sum of copies of the ring.

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Related words

free module

Noun
Japanese Meaning
基底を持つ加群 – すなわち、加群の全ての元がその基底の線形結合として一意に表される加群。 / 環の元からなる n‐タプルとして表現可能で、余計な恒等式を満たさない加群。 / 同一の環を要素とする直和として表すことができ、その直和の成分数(または基底の元の個数)が階数となる加群。
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主イデアル整域上の任意の自由加群は、その環の直和(複数の同型な因子)に同型である。

Related Words

plural

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