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A /-algebra is equivalently a ring whose characteristic divides n. This is because for every ring R there is a ring homomorphism Z → R {\displaystyle \mathbb {Z} \to R} , and this map factors through Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } if and only if the characteristic of R divides n .
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, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
An algebraic structure is a non-empty set of mathematical objects, such as the integers, together with algebraic operations defined on that set, like addition and multiplication. [2] [a] Algebra explores the laws, general characteristics, and types of algebraic
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.
The twisted cubic is a projective algebraic variety. Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in ...
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, ...
In mathematics, the characteristic equation (or auxiliary equation [1]) is an algebraic equation of degree n upon which depends the solution of a given n th-order differential equation [2] or difference equation.