Last Updated
：2025/12/04
composition algebra
Noun
Japanese Meaning
体上の非可換（必ずしも結合的でない）代数 A と、非退化な二次形式 N が存在し、すべての x, y ∈ A に対して N(xy)=N(x)N(y) が成立する代数。すなわち、乗法と二次形式の間に整合性（乗法的あるいは構成的性質）が認められる代数である。
（ plural ）
Quizzes for review
(algebra) A non-associative (not necessarily associative) algebra, A, over some field, together with a nondegenerate quadratic form, N, such that N(xy) = N(x)N(y) for all x, y ∈ A.
音声機能が動作しない場合はこちらをご確認ください
See correct answer
composition algebra
In his lecture on quadratic forms, the professor explained how a composition algebra over a field is a non-associative algebra A equipped with a nondegenerate quadratic form N satisfying N(xy) = N(x)N(y) for all x, y ∈ A.
See correct answer
In his lecture on quadratic forms, the professor explained how a composition algebra over a field is a non-associative algebra A equipped with a nondegenerate quadratic form N satisfying N(xy) = N(x)N(y) for all x, y ∈ A.
音声機能が動作しない場合はこちらをご確認ください
English - English
Word Edit Setting
- Users who have edit permission for words - All Users
- Screen new word creation
- Screen word edits
- Screen word deletion
- Screen the creation of new headword that may be duplicates
- Screen changing entry name
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Sentence Edit Setting
- Users who have edit permission for sentences - All Users
- Screen sentence deletion
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Quiz Edit Setting
- Users who have edit permission for quizzes - All Users
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
