Koszul modules (and the Omega-growth of modules) over short local algebras
Following the well-established terminology in commutative algebra, any (not necessarily commutative) finite-dimensional local algebra A with radical Jwill be said to be shortprovided J(3)= 0. As in the commutative case, also in general, the asymptotic behavior of the Betti numbers of modules seems to be of interest. As we will see, there are only few possibilities for the growth of the Betti numbers of modules. And there is a class of modules, the Koszul modules, where the Betti numbers can be calculated quite easily. We generalize results which are known for commutative algebras, but some of our results seem to be new also in the commutative case. (c) 2021 Elsevier B.V. All rights reserved.
225
12
Elsevier