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- Algebra_over_a_field abstract "In mathematics, an algebra over a field is a vector space equipped with a bilinear product. An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and thus equipped with a field of scalars. Such an algebra is called here a unital associative algebra for clarity, because there are also nonassociative algebras. In other words, an algebra over a field is a set together with operations of multiplication, addition, and scalar multiplication by elements of the underlying field, that satisfy the axioms implied by "vector space" and "bilinear".One may generalize this notion by replacing the field of scalars by a commutative ring, and thus defining an algebra over a ring.Because of the ubiquity of associative algebras, and because many textbooks teach more associative algebra than nonassociative algebra, it is common for authors to use the term algebra to mean associative algebra. However, this does not diminish the importance of nonassociative algebras, and there are texts that give both structures and names equal priority.".
- Algebra_over_a_field wikiPageID "191788".
- Algebra_over_a_field wikiPageRevisionID "600522293".
- Algebra_over_a_field hasPhotoCollection Algebra_over_a_field.
- Algebra_over_a_field subject Category:Algebras.
- Algebra_over_a_field type Abstraction100002137.
- Algebra_over_a_field type Algebra106012726.
- Algebra_over_a_field type Algebras.
- Algebra_over_a_field type Cognition100023271.
- Algebra_over_a_field type Content105809192.
- Algebra_over_a_field type Discipline105996646.
- Algebra_over_a_field type KnowledgeDomain105999266.
- Algebra_over_a_field type Mathematics106000644.
- Algebra_over_a_field type PsychologicalFeature100023100.
- Algebra_over_a_field type PureMathematics106003682.
- Algebra_over_a_field type Science105999797.
- Algebra_over_a_field comment "In mathematics, an algebra over a field is a vector space equipped with a bilinear product. An algebra such that the product is associative and has an identity is therefore a ring that is also a vector space, and thus equipped with a field of scalars. Such an algebra is called here a unital associative algebra for clarity, because there are also nonassociative algebras.".
- Algebra_over_a_field label "Algebra (structuur)".
- Algebra_over_a_field label "Algebra nad ciałem".
- Algebra_over_a_field label "Algebra over a field".
- Algebra_over_a_field label "Algebra su campo".
- Algebra_over_a_field label "Algebra über einem Körper".
- Algebra_over_a_field label "Algèbre sur un corps".
- Algebra_over_a_field label "Álgebra sobre um corpo".
- Algebra_over_a_field label "Álgebra sobre un cuerpo".
- Algebra_over_a_field label "Алгебра над полем".
- Algebra_over_a_field label "جبر على حقل".
- Algebra_over_a_field label "体上の多元環".
- Algebra_over_a_field sameAs Algebra_(struktura).
- Algebra_over_a_field sameAs Algebra_über_einem_Körper.
- Algebra_over_a_field sameAs Álgebra_sobre_un_cuerpo.
- Algebra_over_a_field sameAs Algèbre_sur_un_corps.
- Algebra_over_a_field sameAs Algebra_su_campo.
- Algebra_over_a_field sameAs 体上の多元環.
- Algebra_over_a_field sameAs Algebra_(structuur).
- Algebra_over_a_field sameAs Algebra_nad_ciałem.
- Algebra_over_a_field sameAs Álgebra_sobre_um_corpo.
- Algebra_over_a_field sameAs m.01b6zb.
- Algebra_over_a_field sameAs Q1000660.
- Algebra_over_a_field sameAs Q1000660.
- Algebra_over_a_field sameAs Algebra_over_a_field.
- Algebra_over_a_field wasDerivedFrom Algebra_over_a_field?oldid=600522293.
- Algebra_over_a_field isPrimaryTopicOf Algebra_over_a_field.