منابع مشابه
Unique Factorization of Ideals in OK
Let K be a number field and OK be the ring of algebraic integers. We discuss the unique factorization of elements of OK into irreducibles and its use in solving Diophantine equations. We then proceed to prove the existence of the unique factorization of ideals of OK into prime ideals.
متن کاملComplete Intersections in Toric Ideals
We present examples which show that in dimension higher than one or codimension higher than two, there exist toric ideals IA such that no binomial ideal contained in IA and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations.
متن کاملApplications of Prime Factorization of Ideals in Number Fields
For a number fieldK, that is, a finite extension of Q, and a prime number p, a fundamental theorem of algebraic number theory implies that the ideal (p) ⊆ OK factors uniquely into prime ideals as (p) = p1 1 · · · p eg g . In this paper we explore different interpretations of this using the factorization of polynomials in finite and p-adic fields and Galois theory. In particular, we present some...
متن کاملLocally Complete Intersection Stanley–reisner Ideals
In this paper, we prove that the Stanley–Reisner ideal of any connected simplicial complex of dimension ≥ 2 that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley–Reisner ideal whose powers are Buchsbaum is a complete intersection ideal.
متن کاملRing graphs and complete intersection toric ideals
We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideal...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90286-4