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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper we show that any nonstandard model $Z^{star}$ of Z is isomorphic to $F_{beta}Z$ for some $beta$: F $rightarrow hat{Z}$ where F=$Z^{star}$/Z.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $hat{Z}$ denote the inverse limit of finite cyclic groups and $F_g Z$ the group where F is a vector space over Q and + is defined by (a, x)+(b, y)=(a+b, x+y+g(a,b)) for some g: F$times$ F $rightarrow$ Z.
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Key Findings & Data:Let $hat{Z}$ denote the inverse limit of finite cyclic groups and $F_g Z$ the group where F is a vector space over Q and + is defined by (a, x)+(b, y)=(a+b, x+y+g(a,b)) for some g: F$times$ F $rightarrow$ Z.
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Conclusion & Impact:In this paper we show that any nonstandard model $Z^{star}$ of Z is isomorphic to $F_{beta}Z$ for some $beta$: F $rightarrow hat{Z}$ where F=$Z^{star}$/Z.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let $hat{Z}$ denote the inverse limit of finite cyclic groups and $F_g Z$ the group where F is a vector space over Q and + is defined by (a, x)+(b, y)=(a+b, x+y+g(a,b)) for some g: F$times$ F $rightarrow$ Z. In this paper we show that any nonstandard model $Z^{star}$ of Z is isomorphic to $F_{beta}Z$ for some $beta$: F $rightarrow hat{Z}$ where F=$Z^{star}$/Z.
Özet
Bu çalışmada, Z tamsayılar halkasının her nonstandard modelinin toplamsal grup yapısının, Q üzerine bir F vektör uzayı ve bir $beta$: F $rightarrow hat{Z}$ dönüşümü için, $F_{beta}Z$ grubuna eşyapısal olduğunu kanıtlıyoruz.
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Cite This Article
TERZİLER, M., GENCER, Ç. (2022). Z'nin nonstandard modellerinin toplamsal grup yapısı üzerine. Turkish Journal of Mathematics, Cilt: 20 - Sayı: 2, 179–183. https://ajindex.com/articles/140896