Examples of 'associative algebra' in a sentence
Meaning of "associative algebra"
Associative algebra: In mathematics, an associative algebra is a vector space equipped with a binary operation that generalizes the concept of multiplication. The operation is associative, meaning that the terms can be grouped in any way without changing the result
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- A vector space over some field which also has an associative vector-valued multiplication operator between vectors which together with the abelian group feature of the vector space makes a ring.
- A module over a ring together with an associative bilinear module-element-valued operator between module elements which together with the abelian group feature of the module makes a ring.
How to use "associative algebra" in a sentence
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associative algebra
Power associative algebra.
The commutator of two elements a and b of a ring or an associative algebra is defined by.
Every associative algebra is hence also a pre-Lie algebra, as the associator vanishes identically.
Can be endowed with a structure of an associative algebra under the operation of convolution.
An associative algebra forms a ring over "R" and provides a generalization of a ring.
They also form a commutative unital associative algebra over the complex numbers.
In abstract algebra, a representation of a Hopf algebra is a representation of its underlying associative algebra.
In abstract algebra, a representation of an associative algebra is a module for that algebra.
In one sense, associative algebra representations generalize both representations of groups and Lie algebras.
The polynomials with real coefficients form an associative algebra over the reals.
The dimension of the associative algebra A over the field K is its dimension as a K-vector space.
The polynomials with real coefficients form a unitary associative algebra over the reals.
Here an associative algebra is a (not necessarily unital) ring.
Furthermore, is generated as a unital associative algebra by.
Any associative algebra over the field becomes a Lie algebra over with the Lie bracket,,formula 1.
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The complex numbers form a 2-dimensional associative algebra over the real numbers.
In mathematics, Clifford algebras are a type of associative algebra.
This defines an associative algebra over " K.
The square n-by-n matrices with entries from the field K form a unitary associative algebra over K.
It can be, for example, an associative algebra or a Lie algebra.
M ( n, C ), the ring of complex square matrices, is a complex associative algebra.
If R is a ring, then R is an associative algebra over its center.
M ( n, R ), the ring of real square matrices, is a real unitary associative algebra.
Therefore, the quaternions H are a non-commutative associative algebra over the real numbers.
The vector space V {\displaystyle \mathbb {V} } is endowed thereby with an associative algebra structure.
In particular, the 2 × 2 real matrices form an associative algebra useful in plane mapping.
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Examples of using Associative
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Generates an associative section which can be modified
This is useful mainly for associative arrays
Strengthening associative models for industrial development
Examples of using Algebra
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And we have an algebra midterm to study for
Algebra uses a type of ruler to classify numbers
Forget about your algebra and calculus
