Last Updated
：2025/12/04
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。
（ plural ）
Quizzes for review
(algebra) A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)
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free module
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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