﻿ "Euclidean Domain" related terms, short phrases and links

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### DefinitionsUpDw('Definitions','-Abz-');

1. A Euclidean domain is an integral domain which can be endowed with at least one Euclidean function. (Web site)
2. A Euclidean domain is always a principal ideal domain (PID), an integral domain in which every ideal is a principal ideal. (Web site)
3. Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true. (Web site)
4. Also, any Euclidean domain is a PID; the algorithm used to calculate greatest common divisors may be used to find a generator of any ideal. (Web site)

### ConverseUpDw('CONVERSE','-Abz-');

1. Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true. (Web site)

### Integral DomainUpDw('INTEGRAL_DOMAIN','-Abz-');

1. A Euclidean domain is an integral domain which can be endowed with at least one Euclidean function. (Web site)

### PidUpDw('PID','-Abz-');

1. Again, the converse is not true: not every PID is a Euclidean domain. (Web site)
2. Also, any Euclidean domain is a PID; the algorithm used to calculate greatest common divisors may be used to find a generator of any ideal. (Web site)
3. However, not every PID is a Euclidean domain; the ring furnishes a counterexample.

### Euclidean AlgorithmUpDw('EUCLIDEAN_ALGORITHM','-Abz-');

1. In abstract algebra, a Euclidean domain (also called a Euclidean ring) is a type of ring in which the Euclidean algorithm can be used. (Web site)
2. If R is a Euclidean domain then a form of the Euclidean algorithm can be used to compute greatest common divisors.

### Principal Ideal DomainUpDw('PRINCIPAL_IDEAL_DOMAIN','-Abz-');

1. Summary: Euclidean domain = principal ideal domain = unique factorization domain = integral domain = Commutative ring. (Web site)
2. Despite this counterexample, the polynomial ring over any field is always a principal ideal domain and in fact, a Euclidean domain.

### Euclidean DomainUpDw('EUCLIDEAN_DOMAIN','-Abz-');

1. A Euclidean domain is always a principal ideal domain (PID), an integral domain in which every ideal is a principal ideal. (Web site)
2. This is called "division with remainder" or " polynomial long division " and shows that the ring F[ X] is a Euclidean domain. (Web site)
3. Euclidean domain A Euclidean domain is an integral domain in which a degree function is defined so that "division with remainder" can be carried out.

### CategoriesUpDw('Categories','-Abz-');

1. Principal Ideal Domain
2. Euclidean Algorithm
3. Pid
4. Integral Domain
5. Counterexample
6. Books about "Euclidean Domain" in Amazon.com
 Short phrases about "Euclidean Domain"   Originally created: April 04, 2011.   Links checked: January 23, 2013.   Please send us comments and questions by this Online Form   Please click on to move good phrases up.
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