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  2. Algebra - Wikipedia

    en.wikipedia.org/wiki/Algebra

    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.

  3. Field (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Field_(mathematics)

    Basic theorems in analysis hinge on the structural properties of the field of real numbers. Most importantly for algebraic purposes, any field may be used as the scalars for a vector space, which is the standard general context for linear algebra. Number fields, the siblings of the field of rational numbers, are studied in depth in number theory.

  4. Equation - Wikipedia

    en.wikipedia.org/wiki/Equation

    An identity is an equation that is true for all possible values of the variable(s) it contains. Many identities are known in algebra and calculus. In the process of solving an equation, an identity is often used to simplify an equation, making it more easily solvable. In algebra, an example of an identity is the difference of two squares:

  5. Algebraic operation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_operation

    The ± sign means the equation can be written with either a + or a – sign. In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power). [1]

  6. Norm (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Norm_(mathematics)

    A composition algebra (,,) consists of an algebra over a field, an involution, and a quadratic form = called the "norm". The characteristic feature of composition algebras is the homomorphism property of N {\displaystyle N} : for the product w z {\displaystyle wz} of two elements w {\displaystyle w} and z {\displaystyle z} of the composition ...

  7. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    A Boolean algebra can be interpreted either as a special kind of ring (a Boolean ring) or a special kind of distributive lattice (a Boolean lattice). Each interpretation is responsible for different distributive laws in the Boolean algebra. Similar structures without distributive laws are near-rings and near-fields instead of rings and division ...

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