integral domain वाक्य
उदाहरण वाक्य
मोबाइल
- Over a Noetherian integral domain, torsion-free modules are the modules whose only associated prime is 0.
- Similarly, an integral domain is a Dedekind domain if and only if every divisible module over it is injective.
- Vieta's formulas are frequently used with polynomials with coefficients in any integral domain " R ".
- As explained above, neither primitivity nor irreducibility statement of Gauss's lemma is valid over general integral domains.
- The image of \ varphi is a subring of " L ", and thus an integral domain.
- The theory is simpler for affine rings, which are integral domains that are finitely generated algebras over a field.
- Over a general integral domain, we still have one implication : every injective module over an integral domain is divisible.
- Over a general integral domain, we still have one implication : every injective module over an integral domain is divisible.
- Pr�fer domains can be characterized as integral domains whose totally ordered abelian group is the value group of some valuation domain.
- The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain.
- Integral domains are characterized by the condition that they are irreducible ( that is there is only one minimal prime ideal ).
- In scheme theory, the spectrum of an integral domain has a unique generic point, which is the minimal prime ideal.
- In algebraic geometry, taking the spectrum of a ring whose reduced ring is an integral domain is an irreducible topological space.
- They both noticed it was precisely the extra piece of structure needed to turn an integral domain into a principal ideal domain.
- A "'Euclidean domain "'is an integral domain which can be endowed with at least one Euclidean function.
- An integral domain where a gcd exists for any two elements is called a GCD domain and thus B�zout domains are GCD domains.
- Since fields are integral domains, this is also a construction for the completion of a field with respect to an absolute value.
- A Euclidean domain is always a principal ideal domain ( PID ), an integral domain in which every ideal is a principal ideal.
- The converse is clear : an integral domain has no nonzero nilpotent elements, and the zero ideal is the unique minimal prime ideal.
- If is an integral domain, then by the same reasoning, the fixed points of Frobenius are the elements of the prime field.
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