Search results
Results from the WOW.Com Content Network
A codomain is part of a function f if f is defined as a triple (X, Y, G) where X is called the domain of f, Y its codomain, and G its graph. [1] The set of all elements of the form f(x), where x ranges over the elements of the domain X, is called the image of f. The image of a function is a subset of its codomain so it might not coincide with it.
In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane is a domain, as is the open unit disk, the open upper half-plane, and so forth. Often, a complex domain serves as the domain of definition for a holomorphic function.
In algebra, a domain is a nonzero ring in which ab = 0 implies a = 0 or b = 0. [1] (Sometimes such a ring is said to "have the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the only right zero divisor). A commutative domain is called an integral domain.
The term domain is also commonly used in a different sense in mathematical analysis: a domain is a non-empty connected open set in a topological space. In particular, in real and complex analysis , a domain is a non-empty connected open subset of the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} or the complex coordinate space C n ...
In biological taxonomy, a domain (/ d ə ˈ m eɪ n / or / d oʊ ˈ m eɪ n /) (Latin: regio [1]), also dominion, [2] superkingdom, realm, or empire, is the highest taxonomic rank of all organisms taken together. It was introduced in the three-domain system of taxonomy devised by Carl Woese, Otto Kandler and Mark Wheelis in 1990. [1]
Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory .
Atomic domain, an integral domain in which every nonzero non-unit is a finite product of irreducible 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 a suitable generalization of the Euclidean algorithm
A commutative ring (not necessarily a domain) with unity satisfying this condition is called a containment-division ring (CDR). [2] Thus a Dedekind domain is a domain that either is a field, or satisfies any one, and hence all five, of (DD1) through (DD5). Which of these conditions one takes as the definition is therefore merely a matter of taste.