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In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Any graded algebra graded by , for example =, has a filtration given by = =. An example of a filtered algebra is the Clifford algebra Cliff ( V , q ) {\displaystyle \operatorname {Cliff} (V,q)} of a vector space V {\displaystyle V} endowed with a quadratic form q . {\displaystyle q.}
Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States , [ 5 ] and builds on their understanding of arithmetic .
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions 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.
Pre-algebra is a common name for a course taught in middle school mathematics in the United States, usually taught in the 6th, 7th, 8th, or 9th grade. [1] The main objective of it is to prepare students for the study of algebra. Uref>"A Leak in the STEM Pipeline: Taking Algebra Early". U.S. Department of Education. November 2018
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).