principal ideal domain
41Greatest common divisor — In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more non zero integers, is the largest positive integer that divides the numbers without a remainder. For …
42Torsion (algebra) — In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Definition Let G be a group. An element g of G is called a torsion element if g has… …
43Minimal prime (commutative algebra) — In mathematics, especially in the area of algebra known as commutative algebra, certain prime ideals called minimal prime ideals play an important role in understanding rings and modules. The notion of height and Krull s Hauptidealsatz use… …
44Bézout'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 …
45Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …
46Elementarteilersatz — In der Algebra bezeichnet man Integritätsbereiche als Hauptidealringe oder Hauptidealbereiche, wenn jedes Ideal ein Hauptideal ist. Die wichtigsten Beispiele für Hauptidealringe sind der Ring der ganzen Zahlen sowie Polynomringe in einer… …
47Hauptidealbereich — In der Algebra bezeichnet man Integritätsbereiche als Hauptidealringe oder Hauptidealbereiche, wenn jedes Ideal ein Hauptideal ist. Die wichtigsten Beispiele für Hauptidealringe sind der Ring der ganzen Zahlen sowie Polynomringe in einer… …
48Hauptidealring — In der Algebra, einem Teilgebiet der Mathematik, bezeichnet man Integritätsringe als Hauptidealringe oder Hauptidealbereiche, wenn jedes Ideal ein Hauptideal ist. Die wichtigsten Beispiele für Hauptidealringe sind der Ring der ganzen Zahlen sowie …
49Zariski topology — In algebraic geometry, the Zariski topology is a particular topology chosen for algebraic varieties that reflects the algebraic nature of their definition. It is due to Oscar Zariski and took a place of particular importance in the field around… …
50Proofs of Fermat's theorem on sums of two squares — Fermat s theorem on sums of two squares asserts that an odd prime number p can be expressed as: p = x^2 + y^2with integer x and y if and only if p is congruent to 1 (mod 4). The statement was announced by Fermat in 1640, but he supplied no proof …
