In [22, 4] a conjecture was posed to the effect that if R → A is a homomorphism of Noetherian rings then the André-Quillen homology on the category of A-modules satisfies: Ds(A|R;−) = 0 for s ≫ 0 implies Ds(A|R;−) = 0 for s ≥ 3. In [28], an extended version of this conjecture was considered for which A is a simplicial commutative R-algebra with Noetherian homotopy such that char(π0A) 6= 0. In a...

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

Over a $d$-dimensional Cohen-Macaulay local ring admitting canonical module the definable closure of class balanced big modules is $d$-cotilting and smallest such containing maximal modules. We describe its cotilting structure contrast it to largest The enables an implicit classification all classes

We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we briefly discuss the special case of multiplicative actions, that is, actions on group algebras k[Z n ] via an action on Z n .

In this expository paper we survey results proved during the last fifty years that relate Hilbert coefficients e0(I) and e1(I) of an m-primary ideal I in a Cohen-Macaulay local ring (R, m) with depth of the associated graded ring G(I). Several results in this area follow from two theorems of S. Huckaba and T. Marley. These were proved using homological techniques. We provide simple proofs using...

This paper deals with the effective computation of the radical of certain polynomial ideals. Let k be a characteristic zero field, f1, . . . , fn−r ∈ k[X1, . . . , Xn] a regular sequence with d := maxj deg fj , = the generated ideal, √ = its radical, and suppose that the factor ring k[X1, . . . , Xn]/ √ = is a Cohen-Macaulay ring. Under these assumptions we exhibit a single exponential algorith...

Pinched Veronese rings are formed by removing an algebra generator from a subring of polynomial ring. We study the homological properties such rings, including Cohen-Macaulay, Gorenstein, and complete intersection properties. Greco Martino classified Cohen-Macaulayness pinched maximum entry exponent vector monomial; we re-prove their results with semigroup methods correct omission small class e...