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- W2054193886 abstract "Let A be an Artin algebra and e an idempotent element in A. In this paper, we use co-homological conditions on A to control the finitistic dimension of eAe. Such a consideration is of particular interest for understanding the finitistic dimension conjecture. Let us denote the finitistic dimension and global dimension of A by fin.dim(A) and gl.dim(A), respectively. Suppose gl.dim(A)⩽4. Then fin.dim(eAe)<∞ if one of the following conditions holds: (1) A/AeA has representation dimension at most 3; (2) ΩA−3(A) is an A/AeA-module; (3) proj.dim(SA)⩽3 for all simple A/AeA-modules S. This result can be considered as a first step to the question of whether gl.dim(A)⩽4 implies fin.dim(eAe)<∞. Moreover, we show the following: Let A be an arbitrary Artin algebra and e an idempotent element of A such that the ∗-syzygy dimension or the Gorenstein dimension of the eAe-module Ae is finite. If fin.dim(A)<∞, then fin.dim(eAe)<∞." @default.
- W2054193886 created "2016-06-24" @default.
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- W2054193886 date "2008-05-01" @default.
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- W2054193886 title "On the finitistic dimension conjecture, III: Related to the pair <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi>e</mml:mi><mml:mi>A</mml:mi><mml:mi>e</mml:mi><mml:mo>⊆</mml:mo><mml:mi>A</mml:mi></mml:math>" @default.
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- W2054193886 doi "https://doi.org/10.1016/j.jalgebra.2008.01.021" @default.
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