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On the k ‐HFD property in Dedekind domains with small class group
Author(s) -
Chapman Scott T.,
Smith William W.
Publication year - 1992
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015060
Subject(s) - mathematics , dedekind cut , domain (mathematical analysis) , integer (computer science) , combinatorics , group (periodic table) , order (exchange) , product (mathematics) , class (philosophy) , integral domain , discrete mathematics , pure mathematics , field (mathematics) , mathematical analysis , geometry , physics , finance , quantum mechanics , artificial intelligence , computer science , economics , programming language
Let D be an atomic integral domain (i.e., a domain in which each nonzero nonunit of D can be written as a product of irreducible elements) and k any positive integer. D is known as a half factorial domain (HFD) if for any irreducible elements α 1 , …, α n , β 1 , …, β m of D the equality α 1 … α n = β 1 … β m implies that n = m . In [5] the present authors define D to be a k ‐half factorial domain ( k ‐HFD) if the equality above along with the fact that n or m ≤ k implies that n = m . In this paper we consider the k ‐HFD property in Dedekind domains with small class group and prove the following Theorem: if D is a Dedekind domain with class group of order less than 16 then D is k ‐HFD for some integer k > 1, if, and only if, D is HFD.