Historically, commutative algebra, whose foundations were laid by Dedekind, Hilbert,
Noether, and Krull, has developed in step with algebraic geometry, number theory …

This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford
regularity. Koszul algebras, originally introduced by Priddy, are graded K-algebras R whose …

Estimates are obtained for the degrees of minimal syzygies of quotient algebras of
polynomial rings. For a class that includes Koszul algebras in almost all characteristics …

Let $ K $ be an algebraically closed field of characteristc zero. In this paper we study the
isomorphism classes of Artinian Gorenstein local $ K $-algebras with socle degree three by …

Let R be a local ring with maximal ideal m admitting a non-zero element a ∈ m for which the
ideal (0: a) is isomorphic to R/aR. We study minimal free resolutions of finitely generated R …

Extending a notion defined for surjective maps by Blanco, Majadas, and Rodicio, we
introduce and study a class of homomorphisms of commutative noetherian rings, which …

The structure of minimal free resolutions of finite modules M over commutative local rings (R,
𝔪, k) with 𝔪3= 0 and rank k (𝔪2)< rank k (𝔪/𝔪2) is studied. It is proved that over generic R …

A Koszul algebra R is a N-graded K-algebra whose residue field K has a linear free
resolution as an R-module. We present various characterizations of Koszul algebras and …

Given two positive integers e and s we consider Gorenstein Artinian local rings R whose
maximal ideal m satisfies ms≠ 0= m s+ 1 and rank R/m (m/m 2)= e. We say that R is a …

Let R=⊕ i≥ 0Ri be a quadratic standard graded K-algebra. Backelin has shown that R is
Koszul provided dimR2≤ 2. One may wonder whether, under the same assumption, R is …