Geodesic
Quasi-Koszulity and Minimal Horseshoe Lemma
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4
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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.
Classification : Primary: 18G05,16S37; Secondary: 16E30, 16W50. 
@article{BMMS_2012_35_4_a16,
     author = {Jia-Feng L\"u},
     title = {Quasi-Koszulity and {Minimal} {Horseshoe} {Lemma}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a16/}
}
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Jia-Feng Lü. Quasi-Koszulity and Minimal Horseshoe Lemma. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a16/