ON THE CARTAN MATRIX OF A LEFT ARTINIAN RING
ON THE CARTAN MATRIX OF A LEFT ARTINIAN RING
The Cartan matrix \(C\) of a left Artinian ring \(R\) does not contain a sufficient amount of information for deciding whether \(R\) has finite or infinite left global dimension. Nevertheless the matrix \(C\) can give some important information about the global dimension. The main result of this paper gives a lower bound for the left global dimension of \(R\) depending only on the matrix \(C\).
- University of Padua Italy
Artinian rings and modules (associative rings and algebras), left global dimension, Homological dimension in associative algebras, Cartan matrix, left Artinian ring, Representations of associative Artinian rings
Artinian rings and modules (associative rings and algebras), left global dimension, Homological dimension in associative algebras, Cartan matrix, left Artinian ring, Representations of associative Artinian rings
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