22 Übersetzungen
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Anwendungsbeispiele Englisch
weitere Beispiele ...
- In algebraic geometry, an affine algebraic set can be identified with a quotient ring of a polynomial ring in such a way that the points of the algebraic set correspond to the maximal ideals of the ring (this is Hilbert's Nullstellensatz).
- The notion of localization of a ring (in particular the localization with respect to a prime ideal, the localization consisting in inverting a single element and the total quotient ring) is one of the main differences between commutative algebra and the theory of non-commutative rings.
- The notation "L" / "K" is purely formal and does not imply the formation of a quotient ring or quotient group or any other kind of division.
- Every unital ring may be viewed as an additive category with a single object, and the quotient of additive categories defined above coincides in this case with the notion of a quotient ring modulo a two-sided ideal.
- The quotient ring of a Boolean ring modulo a ring ideal corresponds to the factor algebra of the corresponding Boolean algebra modulo the corresponding order ideal.
- occurs on the corresponding quotient ring.
- Thus, it makes sense to speak of the quotient ring "R"/(ker "f").
- When the less complicated number ring is taken to be the ring of integers, Z, then the norm of a nonzero ideal "I" of a number ring "R" is simply the size of the finite quotient ring "R"/"I".
- Then the ring of univariate polynomial differential operators over "R" is the quotient ring [...].
- The quotient ring "B/I" gives the field R of real numbers [...].
- In the quotient ring (algebra) of residue classes modulo ƒ("X"), the multiplication by "X" defines an endomorphism that has the zeros of ƒ("X") as eigenvalues with the corresponding multiplicities.
- With these operations, the residue classes form a commutative ring, the quotient ring of the Gaussian integers by the ideal generated by [...] , which is also traditionally called the "residue class ring modulo" [...] (for more details, see Quotient ring).
© dict.cc English-German dictionary 2024
Enthält Übersetzungen von der TU Chemnitz sowie aus Mr Honey's Business Dictionary (nur Englisch/Deutsch).
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