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The word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. As a single word without an article, "algebra" names a broad part of mathematics. As a single word with an article or in plural, "an algebra" or "algebras" denotes a specific mathematical structure, whose precise definition depends on the author. Usually the structure has an addition, multiplication, and a scalar multiplication (see Algebra over a field). When some authors use the term "algebra", they make a subset of the following additional assumptions: associative, commutative, unital, and/or finite-dimensional. In universal algebra, the word "algebra" refers to a generalization of the above concept, which allows for n-ary operations. With a qualifier, there is the same distinction: Without an article, it means a part of algebra, such as linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves). With an article, it means an instance of some abstract structure, like a Lie algebra, an associative algebra, or a vertex operator algebra. Sometimes both meanings exist for the same qualifier, as in the sentence: Commutative algebra is the study of commutative rings, which are commutative algebras over the integers.

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「代数」という言葉は、単一の単語または修飾子と数学では、いくつかの関連意味を持ちます。 記事がなければ、1 つの単語として「代数」数学の広い部分の名前。 記事または複数の単一の単語として「代数」または「代数」の正確な定義は著者によって異なります特定の数学的構造を表します。U

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The word "algebra" has several related meanings in a single word or a qualifier-math. Articles without a single word and name of a large "algebraic" math. Articles or more single words and "algebra" and "algebraic" exact definition by author unlike

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単語「代数」は、単一の単語または修飾子数学のいくつかの関連の意味を持っています。 1 つの単語と大きな「代数」数学の名前なしの記事。記事以上の単語と「代数」著者とは異なり、「代数」の正確な定義

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Word "algebra" has several single words or qualifier math-related meaning. Large "algebraic" Mathematics with a one word name without articles. Articles over words and exact "algebra", unlike the "algebraic" author-defined

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単語「代数」は、いくつか単一の単語または修飾子の数学関連の意味を持っています。記事なし 1 つの単語の名前を持つ大規模な「代数」数学。言葉と正確な「代数」、「代数」著者定義とは異なり上の記事

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The word "algebra", some have sense of mathematical relations of single words or qualifier. Articles without a large "algebraic" Mathematics with a one word name. Words and exact "algebra", "algebra" author defined is on a different article.

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単語「代数」単一の単語または修飾子の数学関連の意味があります。1 つの単語の名前を持つ大規模な「代数」数学なしの記事。言葉と正確な「代数」、「代数」著者の定義は別の記事。

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The meaning of the word "algebra" single word or qualifier in math-related. A large "algebraic" Mathematics with a one word name without articles. Words and exact "algebra", another article's definition of "algebraic" author.

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「代数」単一単語や数学関連の修飾子の意味。記事なし 1 つの単語の名前を持つ大規模な「代数」数学。言葉は、正確な「代数」、「代数」著者別記事の定義。

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Meaning of "algebraic" single words or math-related. Articles without a large "algebraic" Mathematics with a one word name. Says the exact "algebra", "algebra" author articles by definition.

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「代数」単語や数学関連の意味。1 つの単語の名前を持つ大規模な「代数」数学なしの記事。正確な「代数」、「代数」著者記事によれば定義によって。

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The meaning of the word "algebra" and math-related. A large "algebraic" Mathematics with a one word name without articles. The algebras an exact, according to the author "algebra" by definition.

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「代数」という言葉の意味や数学関連。記事なし 1 つの単語の名前を持つ大規模な「代数」数学。代数の定義では「代数」著者よると、正確な。

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The meaning of the word "algebra" and math-related. Articles without a large "algebraic" Mathematics with a one word name. "Algebra" author by definition of algebra and exact.

INTO JAPANESE

「代数」という言葉の意味や数学関連。1 つの単語の名前を持つ大規模な「代数」数学なしの記事。「代数」代数の定義を作成し、正確な。

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The meaning of the word "algebra" and math-related. A large "algebraic" Mathematics with a one word name without articles. Create a definition of "Algebra Algebra, exactly.

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「代数」という言葉の意味や数学関連。記事なし 1 つの単語の名前を持つ大規模な「代数」数学。定義を作成する"代数代数、正確。

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The meaning of the word "algebra" and math-related. Articles without a large "algebraic" Mathematics with a one word name. Define "algebraic algebra, exactly.

INTO JAPANESE

「代数」という言葉の意味や数学関連。1 つの単語の名前を持つ大規模な「代数」数学なしの記事。定義"代数代数正確。

BACK INTO ENGLISH

The meaning of the word "algebra" and math-related. A large "algebraic" Mathematics with a one word name without articles. Define "algebraic algebra exactly.

INTO JAPANESE

「代数」という言葉の意味や数学関連。記事なし 1 つの単語の名前を持つ大規模な「代数」数学。定義"代数代数正確。

BACK INTO ENGLISH

The meaning of the word "algebra" and math-related. Articles without a large "algebraic" Mathematics with a one word name. Define "algebraic algebra exactly.

INTO JAPANESE

「代数」という言葉の意味や数学関連。1 つの単語の名前を持つ大規模な「代数」数学なしの記事。定義"代数代数正確。

BACK INTO ENGLISH

The meaning of the word "algebra" and math-related. A large "algebraic" Mathematics with a one word name without articles. Define "algebraic algebra exactly.

INTO JAPANESE

「代数」という言葉の意味や数学関連。記事なし 1 つの単語の名前を持つ大規模な「代数」数学。定義"代数代数正確。

BACK INTO ENGLISH

The meaning of the word "algebra" and math-related. Articles without a large "algebraic" Mathematics with a one word name. Define "algebraic algebra exactly.