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central simple algebra
noun
algebra over a field
noun
(algebra)
A
vector
space
(over
some
field)
with
an
additional
binary
operation,
a
vector-valued
product
between
vectors,
which
is
bilinear
over
vector
addition
and
scalar
multiplication.
(N.B.:
such
bilinearity
implies
distributivity
of
the
vector
multiplication
with
respect
to
the
vector
addition,
which
means
that
such
a
vector
space
is
also
a
ring.)
algebra over a ring
noun
(algebra)
A
module
(over
some
ring)
with
an
additional
binary
operation,
a
module-element-valued
product
between
module
elements,
which
is
bilinear
over
module
addition
and
scalar
multiplication.
(N.B.:
such
bilinearity
implies
distributivity
of
the
module
multiplication
with
respect
to
the
module
addition,
which
means
that
such
a
module
is
also
a
ring.)
non-associative algebra
noun
numerical linear algebra
noun
algebraic graph theory
noun
algebraic K-theory
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