associative algebra in a sentence
1) Finite-dimensional associative division algebras over the real numbers are very rare.
2) In mathematics, Clifford algebras are a type of associative algebra .
3) Pierce, Richard S., "associative algebras ".
4) The polynomials with real coefficients form a unital associative algebra over the reals.
associative algebra example sentences
5) The complex numbers form a 2-dimensional unital associative algebra over the real numbers.6) This is a commutative associative algebra and the spectral norm is the supremum norm.
7) To make this extra assumption clear, these associative algebras are called unital algebras.
8) It is an associative algebra .
9) Therefore, the quaternions H are a non-commutative associative algebra over the real numbers.
10) Previous examples are associative algebras .
11) In particular, the 2 × 2 real matrices form an associative algebra useful in plane mapping.
12) The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras.
13) Incidence algebras of locally finite partially ordered sets are unital· associative algebras considered in combinatorics.
14) Alternative, not necessarily associative, division algebras like the octonions correspond to Moufang planes.
example sentences with associative
15) These rings are also Euclidean Hurwitz algebras, of which quaternions are the largest associative algebra .16) In this case __FORMULA__ and __FORMULA__ generate a commutative associative algebra and __FORMULA__, since __FORMULA__.
17) Clifford algebra is the unital associative algebra generated over an underlying vector space equipped with a quadratic form.
18) Among other properties, the universal enveloping algebra is an associative algebra into which __FORMULA__ injectively imbeds.
19) Faith, Carl, "Rings and things and a fine array of twentieth century associative algebra ".
20) In some areas of mathematics, associative algebras are typically assumed to have a multiplicative unit, denoted 1.
21) Such an algebra is called here a unital associative algebra for clarity, because there are also nonassociative algebras.
22) There exists some structure theory for such algebras that generalizes the analogous results for Lie algebras and associative algebras .
23) In 1891 Eduard Study realized that this associative algebra was ideal for describing the group of motions of three-dimensional space.
24) Even though H contains copies of the complex numbers, it is not an associative algebra over the complex numbers.
25) Noncommutative rings and associative algebras (rings that are also vector spaces) are often studied via their categories of modules.
26) With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra .
27) There are three main sorts of algebraic objects for which this can be done: groups, associative algebras and Lie algebras.
How to use associative in a sentence
28) Every Lie algebra can be embedded into one that arises from an associative algebra in this fashion; see universal enveloping algebra.29) An associative algebra is a ring that is also a vector space over a field K . For instance, the set of n -by- n matrices over the real field R has dimension n 2 as a real vector space.
30) These identities are easy to prove in a finite-dimensional (Euclidean) Jordan algebra (see below) or in a special Jordan algebra, i.e. the Jordan algebra defined by a unital associative algebra .
31) The octonions do not form an associative algebra, so "H""r"(O) can only give a Jordan algebra for "r" = 3.
32) By Hurwitz's theorem "A" must be isomorphic to R, C, H or O. The first three are associative division algebras .
33) If the ring "R" is commutative, i.e., its multiplication is commutative, then M("n", "R") is a unitary noncommutative (unless "n" = 1) associative algebra over "R".
34) Hopf algebras provide a way to improve the representation theory of associative algebras, while retaining the representation theory of groups and Lie algebras as special cases.
35) When considering representations of an associative algebra, one can forget the underlying field, and simply regard the associative algebra as a ring, and its representations as modules.
36) When considering representations of an associative algebra, one can forget the underlying field, and simply regard the associative algebra as a ring, and its representations as modules.
37) However, the representation theory of general associative algebras does not have all of the nice properties of the representation theory of groups and Lie algebras.
38) There are several different classes of groups, associative algebras and Lie algebras, and their representation theories all have an individual flavour.
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