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Finitistic dimension of monomial algebras

✍ Scribed by Hongbo Shi

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
126 KB
Volume
264
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

The minimal projective resolution of the left ideal generated by any monomial p in a monomial algebra is described by a combinatorial object, the dimension tree of p. Two algorithms are proposed for computing the desired dimension trees. Determination of finitistic dimensions is then given as one of many homological applications which this idea might have.

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It is shown that, given any left artinian ring \(A\) which has vanishing radical cube and \(n\) isomorphism classes of simple left modules, the global dimension of \(A\) is either infinite or bounded above by \(n^{2}-n\), and the left finitistic dimension of \(A\) is always less than or equal to \(n

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dedicated to professor rΓΌdiger gΓΆbel on his 60th birthday Let R be a ring and let simp-R be a representative set of all simple (right R-) modules. Denote by <Ο‰ the class of all modules which are finitely generated and have finite projective dimension. The little finitistic dimension of R is defined