bilinear product is <span class="searchmatch">associative</span>. Synonym: linear <span class="searchmatch">algebra</span> Hypernyms: <span class="searchmatch">algebra</span> over a ring, non-<span class="searchmatch">associative</span> <span class="searchmatch">algebra</span> Hyponyms: <span class="searchmatch">algebraic</span> number field, Boolean...
power-<span class="searchmatch">associative</span> <span class="searchmatch">algebra</span> (plural power-<span class="searchmatch">associative</span> <span class="searchmatch">algebras</span>) (<span class="searchmatch">algebra</span>) An <span class="searchmatch">algebra</span> such that every subalgebra generated by one element is <span class="searchmatch">associative</span>. alternative...
An algebra over a ring (or more narrowly, an <span class="searchmatch">algebra</span> over a field) whose bilinear product is not necessarily <span class="searchmatch">associative</span>. Hyponym: <span class="searchmatch">associative</span> <span class="searchmatch">algebra</span>...
alternative <span class="searchmatch">algebra</span> (plural alternative <span class="searchmatch">algebras</span>) (<span class="searchmatch">algebra</span>) An <span class="searchmatch">algebra</span> such that every subalgebra generated by two elements is <span class="searchmatch">associative</span>. Translations...
<span class="searchmatch">associative</span> <span class="searchmatch">algebras</span> plural of <span class="searchmatch">associative</span> <span class="searchmatch">algebra</span>...
power-<span class="searchmatch">associative</span> <span class="searchmatch">algebras</span> plural of power-<span class="searchmatch">associative</span> <span class="searchmatch">algebra</span>...
an <span class="searchmatch">algebra</span> is in particular a vector space. <span class="searchmatch">algebra</span> k-<span class="searchmatch">algebra</span> ring vector space <span class="searchmatch">associative</span> <span class="searchmatch">algebra</span> division <span class="searchmatch">algebra</span> non-<span class="searchmatch">associative</span> <span class="searchmatch">algebra</span> <span class="searchmatch">algebra</span> over...
polynomial <span class="searchmatch">algebra</span> (plural polynomial <span class="searchmatch">algebras</span>) (<span class="searchmatch">algebra</span>) polynomial ring <span class="searchmatch">associative</span> <span class="searchmatch">algebra</span>...
R) equipped with a bilinear binary operation taking values in R. R-<span class="searchmatch">algebra</span> <span class="searchmatch">associative</span> <span class="searchmatch">algebra</span> non-<span class="searchmatch">associative</span> <span class="searchmatch">algebra</span> group ring <span class="searchmatch">algebra</span> over a field...
based on a same underlying finite-dimensional vector space. The <span class="searchmatch">associative</span> <span class="searchmatch">algebra</span> of sums and exterior products of scalars, vectors, blades, multivectors...