کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9497190 1630753 2005 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
How rigid are reduced products?
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
How rigid are reduced products?
چکیده انگلیسی
For any cardinal μ let Zμ be the additive group of all integer-valued functions f:μ⟶Z. The support of f is [f]={i∈μ:f(i)=fi≠0}. Also let Zμ=Zμ/Z<μ with Z<μ={f∈Zμ:|[f]|<μ}. If μ⩽χ are regular cardinals we analyze the question when Hom(Zμ,Zχ)=0 and obtain a complete answer under GCH and independence results in Section 8. These results and some extensions are applied to a problem on groups: Let the norm ∥G∥ of a group G be the smallest cardinal μ with Hom(Zμ,G)≠0-this is an infinite, regular cardinal (or ∞). As a consequence we characterize those cardinals which appear as norms of groups. This allows us to analyze another problem on radicals: The norm ∥R∥ of a radical R is the smallest cardinal μ for which there is a family {Gi:i∈μ} of groups such that R does not commute with the product ∏i∈μGi. Again these norms are infinite, regular cardinals and we show which cardinals appear as norms of radicals. The results extend earlier work (Arch. Math. 71 (1998) 341-348; Pacific J. Math. 118 (1985) 79-104; Colloq. Math. Soc. János Bolyai 61 (1992) 77-107) and a seminal result by Łoś on slender groups. (His elegant proof appears here in new light; Proposition 4.5.), see Fuchs [Vol. 2] (Infinite Abelian Groups, vols. I and II, Academic Press, New York, 1970 and 1973). An interesting connection to earlier (unpublished) work on model theory by (unpublished, circulated notes, 1973) is elaborated in Section 3.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 202, Issues 1–3, 1 November 2005, Pages 230-258
نویسندگان
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