English-Hindi > algebraic integer" sentence in Hindi
algebraic integer in a sentence
Examples 11. In particular, an algebraic integer is an integral element of a finite extension K / \ mathbb { Q }. 12. A special case of-rational points are those that belong to a ring of algebraic integers existing inside the field. 13. The integral closure is nothing else than the ring \ overline { \ textbf { Z } } of all algebraic integers . 14. Since the eigenvalues of a matrix are the roots of the polynomial, the eigenvalues of an integer matrix are algebraic integers . 15. While every number ring is a Dedekind domain, their union, the ring of algebraic integers , is a Pr�fer domain. 16. In algebraic number theory, the rings of algebraic integers are Dedekind rings, which constitute therefore an important class of commutative rings. 17. In particular, in a B�zout domain, prime ( but as the algebraic integer example shows, they need not exist ). 18. The set of all algebraic integers ,, is closed under addition and multiplication and therefore is a commutative subring of the complex numbers. 19. However there is a unique factorization for ideals, which is expressed by the fact that every ring of algebraic integers is a Dedekind domain. 20. For instance the ring of analytic functions on any noncompact Riemann surface is a B�zout domain,, and the ring of algebraic integers is B�zout.
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