Volume 35 • Number 4 • 2012   • Quasi-Koszulity and Minimal Horseshoe Lemma Jia-Feng Lü Abstract. In this paper, we mainly concentrate on the criteria for minimal Horseshoe Lemma to be true in the category of quasi-$\delta$-Koszul modules, denoted by $\mathcal{Q}^{\delta}(R)$. More precisely, for a given short exact sequence $\xi: 0 \rightarrow K \rightarrow M \rightarrow N \rightarrow 0$ in $\mathcal{Q}^{\delta}(R)$, we show that $JK=K\cap JM$ if and only if minimal Horseshoe Lemma holds with respect to $\xi$. Moreover, some applications of minimal Horseshoe Lemma are also given. 2010 Mathematics Subject Classification: Primary: 18G05,16S37; Secondary: 16E30, 16W50. Full text: PDF