euclidean domain वाक्य
उदाहरण वाक्य
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- This led to modern abstract algebraic notions such as Euclidean domains.
- The unique factorization of Euclidean domains is useful in many applications.
- The quadratic integer rings are helpful to illustrate Euclidean domains.
- The rings for which such a theorem exists are called Euclidean domains.
- This algorithm and the associated proof may also be extended to any Euclidean domain.
- Again, the converse is not true : not every PID is a Euclidean domain.
- All Euclidean domains are principal ideal domains.
- Any Euclidean domain is a unique factorization domain ( UFD ), although the converse is not true.
- Important examples are polynomial rings over the integers or over a field, Euclidean domains and principal ideal domains.
- Examples of Euclidean domains include fields, polynomial rings in one variable over a field, and the Gaussian integers.
- It is important to compare the class of Euclidean domains with the larger class of principal ideal domains ( PIDs ).
- B�zout's identity, and therefore the previous algorithm, can both be generalized to the context of Euclidean domains.
- Since the ring of polynomials over a field is a Euclidean domain, we may compute these GCDs using the Euclidean algorithm.
- Since the ring of polynomials over a field is an Euclidean domain, we may compute these GCDs using the Euclidean algorithm.
- A "'Euclidean domain "'is an integral domain which can be endowed with at least one Euclidean function.
- Strictly speaking it is the ring of integers that is Euclidean since fields are trivially Euclidean domains, but the terminology is standard.
- The third condition is a slight generalisation of condition ( EF1 ) of Euclidean functions, as defined in the Euclidean domain article.
- The fundamental theorem of arithmetic applies to any Euclidean domain : Any number from a Euclidean domain can be factored uniquely into irreducible elements.
- The fundamental theorem of arithmetic applies to any Euclidean domain : Any number from a Euclidean domain can be factored uniquely into irreducible elements.
- A Euclidean domain is always a principal ideal domain ( PID ), an integral domain in which every ideal is a principal ideal.
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