on: <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> <span class="searchmatch">ring</span> Wikipedia <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> <span class="searchmatch">ring</span> (plural <span class="searchmatch">algebras</span> <span class="searchmatch">over</span> <span class="searchmatch">rings</span>) (<span class="searchmatch">algebra</span>) <span class="searchmatch">A</span> module (<span class="searchmatch">over</span> <span class="searchmatch">a</span> commutative <span class="searchmatch">ring</span> R) equipped with <span class="searchmatch">a</span> bilinear...
<span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field Wikipedia <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field (plural <span class="searchmatch">algebras</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field) (<span class="searchmatch">algebra</span>) An <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> <span class="searchmatch">ring</span> such that the <span class="searchmatch">ring</span> is in fact <span class="searchmatch">a</span> field...
associative <span class="searchmatch">algebra</span> Wikipedia associative <span class="searchmatch">algebra</span> (plural associative <span class="searchmatch">algebras</span>) (<span class="searchmatch">algebra</span>) An <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> <span class="searchmatch">ring</span> (or more narrowly, an <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field)...
<span class="searchmatch">algebras</span> <span class="searchmatch">over</span> <span class="searchmatch">rings</span> plural of <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> <span class="searchmatch">ring</span>...
reduced <span class="searchmatch">algebra</span> (plural reduced <span class="searchmatch">algebras</span>) (<span class="searchmatch">algebra</span>, <span class="searchmatch">ring</span> theory) An <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> reduced <span class="searchmatch">ring</span>....
non-associative <span class="searchmatch">algebra</span> Wikipedia non-associative <span class="searchmatch">algebra</span> (plural non-associative <span class="searchmatch">algebras</span>) (<span class="searchmatch">algebra</span>) An <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> <span class="searchmatch">ring</span> (or more narrowly, an <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field)...
it has a multiplicative inverse. (It is not required to have a unity element.) Hypernyms: <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field, <span class="searchmatch">ring</span>, vector space Hyponym: octonions...
k-<span class="searchmatch">algebra</span> (plural k-<span class="searchmatch">algebras</span>) (<span class="searchmatch">algebra</span>) An <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field; <span class="searchmatch">a</span> <span class="searchmatch">ring</span> with identity together with an injective <span class="searchmatch">ring</span> homomorphism from <span class="searchmatch">a</span> field, k, to...
multiplication of matrices, matrix multiplication, and matrix inversion. (<span class="searchmatch">algebra</span>) <span class="searchmatch">A</span> matrix <span class="searchmatch">ring</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> commutative <span class="searchmatch">ring</span>. Hypernym: associative <span class="searchmatch">algebra</span>...
structures <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> field (“vector space <span class="searchmatch">over</span> <span class="searchmatch">a</span> field”) and <span class="searchmatch">algebra</span> <span class="searchmatch">over</span> <span class="searchmatch">a</span> <span class="searchmatch">ring</span> (“module <span class="searchmatch">over</span> <span class="searchmatch">a</span> commutative <span class="searchmatch">ring</span>”). (formal structure of <span class="searchmatch">a</span> carrier...