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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.
An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
In mathematics, an algebraic structure or algebraic system [1] consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satisfy.
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. [ 1 ] [ 2 ] For example, in a signature consisting of a single binary operation , the term algebra over a set X of variables is exactly the free magma generated by X .
In this regard, the algebraic closure of F q, is exceptionally simple. It is the union of the finite fields containing F q (the ones of order q n ). For any algebraically closed field F of characteristic 0 , the algebraic closure of the field F (( t )) of Laurent series is the field of Puiseux series , obtained by adjoining roots of t .
Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term). mathematics See mathematics. multivalued A "multivalued function” from a set A to a set B is a function from A to the subsets of B.
An algebraic operation may also be defined more generally as a function from a Cartesian power of a given set to the same set. [9] The term algebraic operation may also be used for operations that may be defined by compounding basic algebraic operations, such as the dot product.
In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial, + +, The number 3 is a constant term. [1]