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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 $D\Lambda$.
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참고문헌 (12)
참고문헌 신청
A. Beligiannis / Some ghost lemmas, survey for `The representation dimension of Artin algebras'
A. Bondal / 2003 / Generators and representability of functors in com-mutative and noncommutative geometry / Mosc. Math. J 3(1):1~36
H. Dao / 2014 / The radius of a subcategory of modules / Algebra Number Theory 8(1):141~172
F. Huard / 2013 / Layer lengths, torsion theories and the nitistic dimension / Appl. Categ. Structures 21(4):379~392
O. Iyama / 2003 / Rejective subcategories of Artin algebras and orders / arXiv:math/0311281
A. Bondal / 2003 / Generators and representability of functors in com-mutative and noncommutative geometry / Mosc. Math. J 3(1):1~36
H. Dao / 2014 / The radius of a subcategory of modules / Algebra Number Theory 8(1):141~172
F. Huard / 2013 / Layer lengths, torsion theories and the nitistic dimension / Appl. Categ. Structures 21(4):379~392
O. Iyama / 2003 / Rejective subcategories of Artin algebras and orders / arXiv:math/0311281
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