Dominio de ideales principales

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Dominio de ideales principales

Definición

Artículo WikipediaFuente Dbpedia

In abstract algebra, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element. More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors (e.g., Bourbaki) refer to PIDs as principal rings. The distinction is that a principal ideal ring may have zero divisors whereas a principal ideal domain cannot. Principal ideal domains are thus mathematical objects which behave somewhat like the integers, with respect to divisibility: any element of a PID has a unique decomposition into prime elements (so an analogue of the fundamental theorem of arithmetic holds); any two elements of a PID have a greatest common divisor (although it may not be possible to find it using the Euclidean algorithm). If x and y are elements of a PID without common divisors, then every element of the PID can be written in the form ax + by.Principal ideal domains are noetherian, they are integrally closed, they are unique factorization domains and Dedekind rings. All Euclidean domains and all fields are principal ideal domains. Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields

Wikipedia Inglés http://en.wikipedia.org/wiki/Principal_ideal_domain

Wikipedia Español http://es.wikipedia.org/wiki/Dominio_de_ideales_principales

Enlaces externos relacionado http://mathworld.wolfram.com/PrincipalRing.html