منابع مشابه
Krull Dimensions of Rings of Holomorphic Functions
We prove that the Krull dimension of the ring of holomorphic functions of a connected complex manifold is at least the cardinality of continuum if and only if it is > 0. Let R be a commutative ring. Recall that the Krull dimension dim(R) of R is the supremum of cardinalities lengths of chains of distinct proper prime ideals in R. Our main result is: Theorem 1. Let M be a connected complex manif...
متن کاملCharacterizations of Krull Rings with Zero Divisors
We show that a ring is a Krull ring if and only if every nonzero regular prime ideal contains a t-invertible prime ideal if and only if every proper regular principal ideal is quasi-equal to a product of prime ideals.
متن کاملDynamical Systems Arising from Units in Krull Rings
To a countable Krull ring R and collection of units ξ1, . . . , ξd ∈ R we associate a Zd–action by automorphisms of the compact abelian group X = R̂. We aim to generalize the framework of an ‘S–integer’ dynamical system as described by Chothi, Everest and Ward. We examine the extent to which some of their results extend to Zd–actions (d ≥ 2) and investigate the relationship between algebraic pro...
متن کاملOn Gröbner bases and Krull dimension of residue class rings of polynomial rings over integral domains
Given an ideal a in A[x1, . . . , xn] where A is a Noetherian integral domain, we propose an approach to compute the Krull dimension of A[x1, . . . , xn]/a, when the residue class ring is a free A-module. When A is a field, the Krull dimension of A[x1, . . . , xn]/a has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetheri...
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: Pacific Journal of Mathematics
سال: 1980
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1980.89.131