NOTE ON GRADED IDEALS WITH LINEAR FREE RESOLUTION AND LINEAR QUOTIENS IN THE EXTERIOR ALGEBRA

Tóm tắt

The goal of this note is to study graded ideals with linear free resolution and linear quotients in the exterior algebra. We use an extension of the notion
of linear quotients, namely componentwise linear quotients, to give another proof
of the well-known result that an ideal with linear quotients is componentwise
linear. After that, we consider special cases where a product of linear ideals has
a linear free resolution.