integral domain उदाहरण वाक्य

उदाहरण वाक्य

1. Integral domains are characterized by the condition that they are irreducible ( that is there is only one minimal prime ideal ).
2. In scheme theory, the spectrum of an integral domain has a unique generic point, which is the minimal prime ideal.
3. In algebraic geometry, taking the spectrum of a ring whose reduced ring is an integral domain is an irreducible topological space.
4. They both noticed it was precisely the extra piece of structure needed to turn an integral domain into a principal ideal domain.
5. A "'Euclidean domain "'is an integral domain which can be endowed with at least one Euclidean function.
6. An integral domain where a gcd exists for any two elements is called a GCD domain and thus B�zout domains are GCD domains.
7. Since fields are integral domains, this is also a construction for the completion of a field with respect to an absolute value.
8. A Euclidean domain is always a principal ideal domain ( PID ), an integral domain in which every ideal is a principal ideal.
9. The converse is clear : an integral domain has no nonzero nilpotent elements, and the zero ideal is the unique minimal prime ideal.
10. If is an integral domain, then by the same reasoning, the fixed points of Frobenius are the elements of the prime field.