Actions of formal groups on special quotients of algebras

Let k be a field of characteristic p > 0 and let F be a one dimensional commutative formal group over k. The endomorphisms of a k-algebra A that defines an action of F on A when A is isomorphic to the quotient B/pB, with B torsion free Zalgebra, are studied

Classification of Cohen-Macaulay tt-spread lexsegment ideals via simplicial complexes

We study the minimal primary decomposition of completely $t$-spread lexsegment ideals via simplicial complexes. We determine some algebraic invariants of such a class of $t$-spread ideals. Hence, we classify all $t$-spread lexsegment ideals which are Cohen-Macaulay.Comment: To appear in Illinois Journal of Mathematic

Linear resolutions of tt-spread lexsegment ideals via Betti splittings

Let $S=K[x_1,\dots,x_n]$ be a polynomial ring in $n$ variables with coefficients over a field $K$. A $t$-spread lexsegment ideal $I$ of $S$ is a monomial ideal generated by a $t$-spread lexsegment set. We determine all $t$-spread lexsegment ideals with linear resolution by means of Betti splittings. As applications we provide formulas for the Betti numbers of such a class of ideals and furthermore we characterize all incompletely $t$-spread lexsegment ideals with linear quotients.Comment: Accepted for publication in the Journal of Algebra and its Application