Smooth algebras and vanishing of Hochschild homology.
This article is a brief survey of the recent results obtained by several authors on Hochschild homology of commutative algebras arising from the second author’s paper [21].
In this note we study some algebraic properties of Borel Ideals in the ring of polynomials over an effective field of characteristic zero by using a suitable partial order relation defined on the set of terms of each degree. In particular, in the three variable case, we characterize all the 0-dimensional Borel ideals corresponding to an admissible -vector and their minimal free resolutions.