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searching for Noncommutative ring 13 found (37 total)

Maximal ideal (1,488 words) [view diff] exact match in snippet view article find links to article

special case of unital commutative rings they are also fields. In noncommutative ring theory, a maximal right ideal is defined analogously as being a maximal

Opposite ring (3,535 words) [view diff] exact match in snippet view article find links to article

such ring R {\displaystyle R} has eight elements and it is the only noncommutative ring among 11 rings with unity of order 8, up to isomorphism. It has the

Dense submodule (1,016 words) [view diff] exact match in snippet view article find links to article

extension". Dense submodules are connected with rings of quotients in noncommutative ring theory. Most of the results appearing here were first established

Quaternionic matrix (616 words) [view diff] exact match in snippet view article find links to article

a matrix whose elements are quaternions. The quaternions form a noncommutative ring, and therefore addition and multiplication can be defined for quaternionic

Prime ideal (2,642 words) [view diff] no match in snippet view article find links to article

found in texts such as Goodearl's and Lam's. If R is a (possibly noncommutative) ring and P is a proper ideal of R, we say that P is prime if for any two

Semisimple module (1,249 words) [view diff] exact match in snippet view article find links to article

many other nice examples are discussed in more detail in several noncommutative ring theory texts, including chapter 3 of Lam's text, in which they are

Linear combination (2,666 words) [view diff] exact match in snippet view article find links to article

call spaces like this V modules instead of vector spaces. If K is a noncommutative ring, then the concept still generalizes, with one caveat: since modules

Connection (algebraic framework) (960 words) [view diff] exact match in snippet view article

bundles. Superconnections always exist. If A {\displaystyle A} is a noncommutative ring, connections on left and right A-modules are defined similarly to

Donald S. Passman (618 words) [view diff] exact match in snippet view article find links to article

(2001–2016). His research interests include finite and infinite groups, noncommutative ring theory, group rings and enveloping algebras of Lie algebras. In 1963

Abstract algebra (4,175 words) [view diff] exact match in snippet view article find links to article

abstract groups was O. K. Schmidt's 1916 Abstract Theory of Groups. Noncommutative ring theory began with extensions of the complex numbers to hypercomplex

Gene Abrams (972 words) [view diff] case mismatch in snippet view article find links to article

Oregon, Ph.D. (1981) Scientific career Fields Mathematics, Algebra, Noncommutative Ring Theory, Morita Equivalence, Leavitt Path Algebras Institutions University

Semilinear map (2,059 words) [view diff] exact match in snippet view article find links to article

collected into the following result. Let R {\displaystyle R} be a noncommutative ring, M {\displaystyle M} a left R {\displaystyle R} -module, and α {\displaystyle

Differential algebra (7,846 words) [view diff] exact match in snippet view article find links to article

}}j\neq k,\ p_{j}(c)=0{\text{ with }}c\in K} The associative, possibly noncommutative ring A {\textstyle A} has derivation d : A → A {\textstyle d:A\to A}