enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Domain of a function - Wikipedia

   en.wikipedia.org/wiki/Domain_of_a_function

   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 ...

3. Domain (ring theory) - Wikipedia

   en.wikipedia.org/wiki/Domain_(ring_theory)

   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.

4. Domain (mathematical analysis) - Wikipedia

   en.wikipedia.org/wiki/Domain_(mathematical_analysis)

   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.

5. Linear equation over a ring - Wikipedia

   en.wikipedia.org/wiki/Linear_equation_over_a_ring

   Let R be an effective commutative ring.. There is an algorithm for testing if an element a is a zero divisor: this amounts to solving the linear equation ax = 0.; There is an algorithm for testing if an element a is a unit, and if it is, computing its inverse: this amounts to solving the linear equation ax = 1.

6. Function (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Function_(mathematics)

   Given its domain and its codomain, a function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. [note 1] [4] When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.

7. Unique factorization domain - Wikipedia

   en.wikipedia.org/wiki/Unique_factorization_domain

   A Noetherian integral domain is a UFD if and only if every height 1 prime ideal is principal (a proof is given at the end). Also, a Dedekind domain is a UFD if and only if its ideal class group is trivial. In this case, it is in fact a principal ideal domain. In general, for an integral domain A, the following conditions are equivalent: A is a UFD.