On the extension dimension of module categories
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Let $\Lambda$ be an Artin algebra and $\mod \Lambda$ the category of finitely generated right $\Lambda$-modules. We prove that the radical layer length of $\Lambda$ is an upper bound for the radical layer length of $\mod \Lambda$. We give an upper bound for the extension dimension of $\mod \Lambda$ in terms of the injective dimension of a certain class of simple right $\Lambda$-modules and the radical layer length of $D\Lambda$.
Abstract
Let $\Lambda$ be an Artin algebra and $\mod \Lambda$ the category of finitely generated right $\Lambda$-modules. We prove that the radical layer length of $\Lambda$ is an upper bound for the radical layer length of $\mod \Lambda$. We give an upper bound for the extension dimension of $\mod \Lambda$ in terms of the injective dimension of a certain class of simple right $\Lambda$-modules and the radical layer length of $D\Lambda$.
참고문헌 (12)
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