Algebra - Wikipedia
网页Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.
Algebra I - Khan Academy
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Algebra over a field - Wikipedia
网页In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space ...
Algebra - Stanford Encyclopedia of Philosophy
网页2007年5月29日 · Algebra is a branch of mathematics sibling to geometry, analysis (calculus), number theory, combinatorics, etc. Although algebra has its roots in numerical domains such as the reals and the complex numbers, in its full generality it differs from its siblings in serving no specific mathematical domain.
Coalgebra - Wikipedia
网页In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams. Turning all arrows around, one obtains the axioms of coalgebras.
ALGEBRA中文(简体)翻译：剑桥词典 - Cambridge Dictionary
网页noun [ U ] uk / ˈæl.dʒə.brə / us / ˈæl.dʒə.brə / Add to word list. a part of mathematics in which signs and letters represent numbers. 代数. 相关词语. algebraically. (algebra在剑桥 …
Algebra -- from Wolfram MathWorld
网页2024年8月22日 · Examples of algebras include the algebra of real numbers, vectors and matrices, tensors, complex numbers, and quaternions. (Note that linear algebra, which is the study of linear sets of equations and their transformation properties, is not an algebra in the formal sense of the word.)
Journal of Algebra | ScienceDirect.com by Elsevier
网页The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are …
Algebras, hyperalgebras, nonassociative bialgebras and loops
网页2007年1月30日 · Sabinin algebras are a broad generalization of Lie algebras that include Lie, Malcev and Bol algebras as very particular examples. We present a construction of a universal enveloping algebra for Sabinin algebras, and the corresponding Poincaré–Birkhoff–Witt Theorem. A nonassociative counterpart of Hopf algebras is also introduced and a ...
网页The algebra k<M>, called the tensor algebra on M, is universal among k-algebras given with k-module homomorphisms of M into them. The algebra ΛM, called the exterior algebra on M, is universal among k-algebras given with