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Anwendungsbeispiele Englisch
weitere Beispiele ...
- In commutative algebra, associated primes are linked to the Lasker–Noether primary decomposition of ideals in commutative Noetherian rings.
- Since PID's are Noetherian rings, this can be seen as a manifestation of the Lasker-Noether theorem.
- Lasker–Noether theorem implies that every algebraic set is the union of a finite number of uniquely defined algebraic sets, called its "irreducible components".
- Noetherian rings are fundamental in both commutative and noncommutative ring theory since many rings that are encountered in mathematics are Noetherian (in particular the ring of integers, polynomial rings, and rings of algebraic integers in number fields), and many general theorems on rings rely heavily on Noetherian property (for example, the Lasker–Noether theorem and the Krull intersection theorem).
- The Lasker–Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings.
- While unique factorization does not hold in [...] , there is unique factorization of ideals. See Lasker–Noether theorem.
© dict.cc English-German dictionary 2024
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