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Additional
algebra over a field
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Algebra over a field
In
mathematics
, an
algebra
is one of the fundamental
algebraic structures
used in
abstract algebra
. An
algebra over a field
is a
vector space
(a
module
over a
field
) equipped with a
bilinear
product
. Thus, 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".
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