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integer ring

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  • Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

  • Integer — This article is about the mathematical concept. For integers in computer science, see Integer (computer science). Symbol often used to denote the set of integers The integers (from the Latin integer, literally untouched , hence whole : the word… …   Wikipedia

  • Ring of integers — In mathematics, the ring of integers is the set of integers making an algebraic structure Z with the operations of integer addition, negation, and multiplication. It is a commutative ring, and is the prototypical such by virtue of satisfying only …   Wikipedia

  • Integer-valued polynomial — In mathematics, an integer valued polynomial P(t) is a polynomial taking an integer value P(n) for every integer n . Certainly every polynomial with integer coefficients is integer valued. There are simple examples to show that the converse is… …   Wikipedia

  • Integer lattice — In mathematics, the n dimensional integer lattice (or cubic lattice), denoted Zn, is the lattice in the Euclidean space Rn whose lattice points are n tuples of integers. The two dimensional integer lattice is also called the square lattice, or… …   Wikipedia

  • Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… …   Wikipedia

  • Noetherian ring — In mathematics, more specifically in the area of modern algebra known as ring theory, a Noetherian ring, named after Emmy Noether, is a ring in which every non empty set of ideals has a maximal element. Equivalently, a ring is Noetherian if it… …   Wikipedia

  • Algebraic integer — This article deals with the ring of complex numbers integral over Z. For the general notion of algebraic integer, see Integrality .In number theory, an algebraic integer is a complex number which is a root of some monic polynomial (leading… …   Wikipedia

  • Eisenstein integer — In mathematics, Eisenstein integers, named after Ferdinand Eisenstein, are complex numbers of the form :z = a + bomega ,!where a and b are integers and:omega = frac{1}{2}( 1 + isqrt 3) = e^{2pi i/3}is a complex cube root of unity. The Eisenstein… …   Wikipedia

  • Gaussian integer — In number theory, a Gaussian integer is a complex number whose real and imaginary part are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. The… …   Wikipedia

  • Kummer ring — In abstract algebra, a Kummer ring mathbb{Z} [zeta] is a subring of the ring of complex numbers, such that each of its elements has the form: n 0 + n 1 zeta + n 2 zeta^2 + ... + n {m 1} zeta^{m 1} where zeta; is an m th root of unity, i.e.: zeta …   Wikipedia

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