dedekind domain वाक्य
उदाहरण वाक्य
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- Thus a Dedekind domain is a domain that satisfies any one, and hence all five, of ( DD1 ) through ( DD5 ).
- *PM : ideal decomposition in Dedekind domain, id = 7219-- WP guess : ideal decomposition in Dedekind domain-- Status:
- *PM : ideal decomposition in Dedekind domain, id = 7219-- WP guess : ideal decomposition in Dedekind domain-- Status:
- However there is a unique factorization for ideals, which is expressed by the fact that every ring of algebraic integers is a Dedekind domain.
- Now we can appreciate ( DD3 ) : in a Dedekind domain and only in a Dedekind domain !-- is every fractional ideal invertible.
- The name " divisor " goes back to the work of Weber, who showed the relevance of Dedekind domains to the study of algebraic curves.
- Taking " R " = " Z " this construction tells us precisely that rings of integers of number fields are Dedekind domains.
- Remarkably, the additional structure in torsionfree finitely generated modules over an arbitrary Dedekind domain is precisely controlled by the class group, as we now explain.
- For a Dedekind domain, this is the case : indeed, K 1 is generated by the images of GL 1 and SL 2 in GL.
- The integral closure of a Dedekind domain in a finite extension of the field of fractions is a Dedekind domain; in particular, a noetherian ring.
- The integral closure of a Dedekind domain in a finite extension of the field of fractions is a Dedekind domain; in particular, a noetherian ring.
- A finite generically �tale extension B / A of Dedekind domains is tame iff the trace \ mathrm { Tr } : B \ to A is surjective.
- However, as for every Dedekind domain, a ring of quadratic integers is a unique factorization domain if and only if it is a principal ideal domain.
- Over a Dedekind domain, a finitely-generated module is torsion-free if and only if it is projective, but is in general not free.
- A Krull domain is a higher-dimensional analog of a Dedekind domain : a Dedekind domain that is not a field is a Krull domain of dimension 1.
- A Krull domain is a higher-dimensional analog of a Dedekind domain : a Dedekind domain that is not a field is a Krull domain of dimension 1.
- A field is a commutative ring in which there are no nontrivial proper ideals, so that any field is a Dedekind domain, however in a rather vacuous way.
- In fact, this property characterizes Dedekind domains : an integral domain is a Dedekind domain if, and only if, every non-zero fractional ideal is invertible.
- In fact, this property characterizes Dedekind domains : an integral domain is a Dedekind domain if, and only if, every non-zero fractional ideal is invertible.
- The group of divisors on a curve ( the free abelian group on its set of points ) is closely related to the group of fractional ideals for a Dedekind domain.
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