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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Let $f:A\rightarrow B$ be a be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we give a characterization for the amalgamation of $A$ with $B$ along $J$ with respect to $f$(denoted by $R$ $\bowtie^{f}$ $J$) to be (uniquely) clean.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $f:A\rightarrow B$ be a be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we give a characterization for the amalgamation of $A$ with $B$ along $J$ with respect to $f$(denoted by $R$ $\bowtie^{f}$ $J$) to be (uniquely) clean.
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Key Findings & Data:Let $f:A\rightarrow B$ be a be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we give a characterization for the amalgamation of $A$ with $B$ along $J$ with respect to $f$(denoted by $R$ $\bowtie^{f}$ $J$) to be (uniquely) clean.
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Conclusion & Impact:Let $f:A\rightarrow B$ be a be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we give a characterization for the amalgamation of $A$ with $B$ along $J$ with respect to $f$(denoted by $R$ $\bowtie^{f}$ $J$) to be (uniquely) clean.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Amalgamated algebra along an ideal · (uniquely) clean rings · neat rings.
Abstract
Let $f:A\rightarrow B$ be a be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we give a characterization for the amalgamation of $A$ with $B$ along $J$ with respect to $f$(denoted by $R$ $\bowtie^{f}$ $J$) to be (uniquely) clean.
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Cite This Article
Chhiti, M., Mahdou, N., Tamekkante, M. (2015). Clean property in amalgamated algebras along an ideal. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 1. https://ajindex.com/articles/1403323