mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations...
20 KB (3,124 words) - 14:07, 23 June 2024
In commutative algebra, an integrally closed domain A is an integral domain whose integral closure in its field of fractions is A itself. Spelled out...
12 KB (1,924 words) - 02:04, 15 July 2024
elements Bézout domain, an integral domain in which the sum of two principal ideals is again a principal ideal Euclidean domain, an integral domain which allows...
6 KB (843 words) - 09:46, 9 August 2024
said to be integral over a subring A of B if b is a root of some monic polynomial over A. If A, B are fields, then the notions of "integral over" and of...
32 KB (5,304 words) - 00:34, 25 August 2024
fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero...
14 KB (1,808 words) - 00:03, 2 September 2024
type of the function as well as the domain over which the integration is performed. For example, a line integral is defined for functions of two or more...
68 KB (9,235 words) - 12:25, 23 August 2024
In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a commutative ring without nonzero zero divisors) in which every ideal...
10 KB (1,446 words) - 11:53, 24 June 2024
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors...
24 KB (3,745 words) - 16:27, 10 June 2024
more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function...
19 KB (2,440 words) - 15:00, 29 May 2024
measures the "size" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping |x| from...
10 KB (1,317 words) - 12:51, 26 March 2024