منابع مشابه
Local and global tameness in Krull monoids
Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then the global tame degree t(H) equals zero if and only if H is factorial (equivalently, |G| = 1). If |G| > 1, then D(G) ≤ t(H) ≤ 1 + D(G) (
متن کاملOn Minimal Distances in Krull Monoids with Infinite Class Group
Let H be a Krull monoid with infinite class group such that each divisor class contains a prime divisor. We show that for every positive integer n, there exists a divisor closed submonoid S of H such that min∆(S) = n.
متن کاملA New Characterization of Half-factorial Krull Monoids
Let M be a Krull monoid. Then every element of M may be written as a finite product of irreducible elements. If for every a ∈ M , each two factorizations of a have the same number of irreducible elements, then M is called half-factorial. Using a property of element exponentiation, we provide a new characterization of half-factoriality, valid for all Krull monoids whose class group has torsion-f...
متن کاملHomomorphisms on Infinite Direct Products of Groups, Rings and Monoids
We study properties of a group, abelian group, ring, or monoid B which (a) guarantee that every homomorphism from an infinite direct product ∏ I Ai of objects of the same sort onto B factors through the direct product of finitely many ultraproducts of the Ai (possibly after composition with the natural map B → B/Z(B) or some variant), and/or (b) guarantee that when a map does so factor (and the...
متن کاملOn the Arithmetic of Krull Monoids with Infinite Cyclic Class Group
Let H be a Krull monoid with infinite cyclic class group G and let GP ⊂ G denote the set of classes containing prime divisors. We study under which conditions on GP some of the main finiteness properties of factorization theory—such as local tameness, the finiteness and rationality of the elasticity, the structure theorem for sets of lengths, the finiteness of the catenary degree, and the exist...
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ژورنال
عنوان ژورنال: Bollettino dell'Unione Matematica Italiana
سال: 2021
ISSN: 1972-6724,2198-2759
DOI: 10.1007/s40574-021-00301-9