principal ideal domain
81Classification theorem — In mathematics, a classification theorem answers the classification problem What are the objects of a given type, up to some equivalence? . It gives a non redundant enumeration: each object is equivalent to exactly one class. A few related issues …
82Obliteration by incorporation — Sociology …
83Structure theorem — may refer to: * Structured program theorem, a result in programming language theory * Structure theorem for finitely generated modules over a principal ideal domain, a result in abstract algebra (a subject area in mathematics) …
84Finitely-generated abelian group — In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. In this case, we …
85PID — Pelvic inflammatory disease (Medical » Physiology) *** Proportional Integral Derivative (Academic & Science » Mathematics) ** Process IDentifier (Computing » Software) * Project Initiation Document (Governmental » Police) * Personal… …
86Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with …
87Glossary of order theory — This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be …
88Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… …
89Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …
90Integrality — In commutative algebra, the notions of an element integral over a ring (also called an algebraic integer over the ring), and of an integral extension of rings, are a generalization of the notions in field theory of an element being algebraic over …
