The conjectures of M. Boij and J. Söderberg [3], proven by D. Eisenbud and F.-O. Schreyer [8] (see also [7, 4]), link the extremal properties of invariants of graded free resolutions of finitely generated modules over the polynomial ring S = k[x1, . . . , xn] with the Herzog–Huneke–Srinivasan Multiplicity Conjectures. Here k is any field and S has the standard Z-grading. In the course of their ...

In this article, we study minimal graded free resolutions of Cohen-Macaulay tangent cones some monomial curves associated to 4-generated pseudo symmetric numerical semigroups. We explicitly give the matrices in these resolutions.

The use of algorithms in algebra as well as the study of their complexity was initiated before the advent of modern computers. Hermann [25] studied the ideal membership problem, i.e determining whether a given polynomial is in a fixed homogeneous ideal, and found a doubly exponential bound on its computational complexity. Later Mayr and Meyer [31] found examples which show that her bound was ne...

free vibration of simply supported circular cylindrical shell made of functionally graded material (fgm) under internal pressure was investigated. the effective material properties are assumed to vary continuously along the thickness direction according to a volume fraction power law distribution. first order shear deformation theory based on love's first approximation theory was utilized in th...

For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...

We already know that the noncommutative N-graded Noetherian algebras resemble commutative local rings in many respects. also have important property every minimal acyclic complex of finitely generated graded free modules is totally acyclic, and we want to generalize such properties algebra. By generalizing conclusions about combining what algebras, identify a class with acyclic. discuss how rel...

In this paper we prove parts of a conjecture of Herzog giving lower bounds on the rank of the free modules appearing in the linear strand of a graded k-th syzygy module over the polynomial ring. If in addition the module is Z n-graded we show that the conjecture holds in full generality. Furthermore, we give lower and upper bounds for the graded Betti numbers of graded ideals with a linear reso...