integral domain
81List of mathematics articles (I) — NOTOC Ia IA automorphism ICER Icosagon Icosahedral 120 cell Icosahedral prism Icosahedral symmetry Icosahedron Icosian Calculus Icosian game Icosidodecadodecahedron Icosidodecahedron Icositetrachoric honeycomb Icositruncated dodecadodecahedron… …
82Valuation ring — In abstract algebra, a valuation ring is an integral domain D such that for every element x of its field of fractions F , at least one of x or x 1 belongs to D .Given a field F , if D is a subring of F such that either x or x 1 belongs to D for… …
83Prime ideal — In mathematics, a prime ideal is a subset of a ring which shares many important properties of a prime number in the ring of integers. This article only covers ideals of ring theory. Prime ideals in order theory are treated in the article on… …
84Prime ring — In abstract algebra, a non trivial ring R is a prime ring if for any two elements a and b of R , if arb = 0 for all r in R , then either a = 0 or b = 0 . Prime ring can also refer to the subring of a field determined by its characteristic. For a… …
85Gauss's lemma (polynomial) — This article is about Gauss s lemma for polynomials. See also Gauss s lemma. In algebra, in the theory of polynomials, Gauss s lemma, named after Carl Friedrich Gauss, is either of two related statements about polynomials with integral… …
86Bézout's identity — In number theory, Bézout s identity for two integers a, b is an expression where x and y are integers (called Bézout coefficients for (a,b)), such that d is a common divisor of a and b. Bézout s lemma states that such coefficients exist for every …
87List of abstract algebra topics — Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this …
88Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… …
89Chinese remainder theorem — The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. In its most basic form it concerned with determining n, given the remainders generated by division of n by several numbers.… …
90Polynomial — In mathematics, a polynomial (from Greek poly, many and medieval Latin binomium, binomial [1] [2] [3], the word has been introduced, in Latin, by Franciscus Vieta[4]) is an expression of finite length constructed from variables (also known as… …
