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This is a list of possibly nonassociative algebras.An algebra is a module, wherein you can also multiply two module elements. (The multiplication in the module is compatible with multiplication-by-scalars from the base ring).
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and ...
This glossary of linear algebra is a list of definitions and terms relevant to the field of linear algebra, the branch of mathematics concerned with linear equations and their representations as vector spaces. For a glossary related to the generalization of vector spaces through modules, see glossary of module theory
Outline of algebra; List of algebraic coding theory topics; List of algebraic constructions; List of algebraic geometry topics; List of algebraic number theory topics; Outline of algebraic structures; List of complex and algebraic surfaces; List of algebras; List of algorithm general topics; List of algorithms; List of terms relating to ...
A linear algebraic group defined over a field is a torus if only if its base change ¯ to an algebraic closure ¯ is isomorphic to a product of multiplicative groups , ¯. G {\displaystyle G} is a split torus if and only if it is isomorphic to G m , k n {\displaystyle G_{m,k}^{n}} without any base change.
Note that many of the terms are completely rigorous in context. almost all A shorthand term for "all except for a set of measure zero", when there is a measure to speak of. For example, "almost all real numbers are transcendental" because the algebraic real numbers form a countable subset of the real numbers with measure zero.
This is a list of notable theorems. Lists of theorems and similar statements include: ... (algebraic groups, representation theory, ... additional terms may apply.
Algebraic closure: If F is a field, then ¯ is its algebraic closure, that is, the smallest algebraically closed field that contains F. For example, Q ¯ {\displaystyle {\overline {\mathbb {Q} }}} is the field of all algebraic numbers .