Related papers: On nearly Gorenstein affine semigroups

We obtain various characterizations of commutative Noetherian local rings $(R, \fm)$ in terms of homological dimensions of certain finitely generated modules. For example, we establish that $R$ is Gorenstein if the Gorenstein injective…

A result of Pyber states that every finite group $G$ contains an abelian subgroup whose order is quasi-polynomially large in $\lvert G\rvert$. We prove a similar result for $K$-approximate subgroups of solvable groups under only modest…

If I is an ideal in a Gorenstein ring S and S/I is Cohen-Macaulay, then the same is true for any linked ideal I'. However, such statements hold for residual intersections of higher codimension only under very restrictive hypotheses, not…

In this paper we study almost Cohen-Macaulay bipartite graphs. Furthermore, we prove that if $G$ is almost Cohen-Macaulay bipartite graph with at least one vertex of positive degree, then there is a vertex of $\deg(v) \leq 2$. In…

In this paper, we give new characterizations of the Buchsbaum and Cohen-Macaulay properties of the tangent cone $\gr_\frakm(R)$, where $(R,\frakm)$ is a numerical semigroup ring of embedding dimension 3. In particular, we confirm the…

Let R = k[[x_0,...,x_d]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x_0,...,x_d]]. We investigate the question of which rings of this form have bounded Cohen--Macaulay type, that is, have a bound…

In this paper we study the isomorphism classes of local, Artinian, Gorenstein k-algebras A whose maximal ideal M satisfies dim_k(M^3/M^4)=1 by means of Macaulay's inverse system generalizing a recent result by J. Elias and M.E. Rossi. Then…

We notice the connection between almost Cohen-Macaulay rings and the Cohen-Macaulay defect. We introduce a Serre-type condition for modules, that is connected to the Cohen-Macaulay defect in the same way that the condition $(S_n)$ is…

Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism…

Let Q be a regular local ring of dimension 3. We show how to trim a Gorenstein ideal in Q to obtain an ideal that defines a quotient ring that is close to Gorenstein in the sense that its Koszul homology algebra is a Poincare duality…

We study some properties of a family of rings $R(I)_{a,b}$ that are obtained as quotients of the Rees algebra associated with a ring $R$ and an ideal $I$. In particular, we give a complete description of the spectrum of every member of the…

Over Cohen--Macaulay rings admitting a pointwise dualizing module, we show that the class of modules of restricted projective dimension bounded by any integer is finitely deconstructible and that the class of modules of restricted flat…

We formulate a new theorem giving several necessary and sufficient conditions in order that a surjection of the fundamental group $\pi_1(X)$ of a compact K\"ahler manifold onto the fundamental group $\Pi_g$ of a compact Riemann surface of…

Let $C$ be a Gorenstein noncomplete intersection monomial curve in the 4-dimensional affine space with defining ideal $I(C)$. In this article, we use the minimal generating set of $I(C)$ to give a criterion for determining whether the…

Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical…

We study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. We show the existence of a recollement of the above quotient category and it has the…

We discuss invariants of Cohen-Macaulay local rings that admit a canonical module $\omega$. Attached to each such ring R, when $\omega$ is an ideal, there are integers--the type of R, the reduction number of $\omega$--that provide valuable…

The Gruenberg-Kegel graph $\Gamma(G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $|G|$ and in which two distinct vertices $r$ and $s$ are adjacent if and only if there exists an element of order $rs$…

A result of Foxby states that if there exists a complex with finite depth, finite flat dimension, and finite injective dimension over a local ring $R$, then $R$ is Gorenstein. In this paper we investigate some homological dimensions…

The question of when the Rees algebra ${\mathcal R} (I)= \bigoplus_{n \ge 0}I^n$ of $I$ is an almost Gorenstein graded ring is explored, where $R$ is a two-dimensional regular local ring and $I$ a contracted ideal of $R$. It is known that…