Integral degree of a ring, reduction numbers and uniform Artin–Rees numbers
نویسندگان
چکیده
منابع مشابه
Integral Degree of a Ring and Reduction Numbers
The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains bounds for the Castelnuovo-Mumford regularity of the Rees algebra and for the Artin-Rees numbers.
متن کامل3-Uniform hypergraphs of bounded degree have linear Ramsey numbers
Chvátal, Rödl, Szemerédi and Trotter [1] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform ‘pseudo-random’ hypergraphs. keywords: hypergraphs; regularity lemm...
متن کاملOn Ramsey numbers of uniform hypergraphs with given maximum degree
For every > 0 and every positive integers Δ and r , there exists C = C( ,Δ, r) such that the Ramsey number, R(H,H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C|V (H)|1+ . © 2006 Elsevier Inc. All rights reserved.
متن کاملTransversal numbers of uniform hypergraphs
The transversal number ~(H) of a hypergraph H is the minimum eardinality of a set of vertices that intersects all edges of H. For k ~ 1 define ck = supz(H)/(ra + n), where H ranges over all k-uniform hypergraphs with n vertices and m edges. Applying probabilistic arguments we show that ck = (1 + o ( 1 ) ) ~ , r . This settles a problem of Tuza. t ~
متن کاملMultiplicities and Reduction Numbers
Let (R,m) be a Cohen–Macaulay local ring and let I be an ideal. There are at least five algebras built on I whose multiplicity data affect the reduction number r(I) of the ideal. We introduce techniques from the Rees algebra theory of modules to produce estimates for r(I), for classes of ideals of dimension one and two. Previous cases of such estimates were derived for ideals of dimension zero.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.10.007