In a perfect category every object has a minimal projective resolution. We give a sufficient condition for the category of modules over a category-graded algebra to be perfect. AMS Subject Classification (2000): 18E15, 16W50. In [6] the second author explored homological properties of algebras graded over a small category. Our interest in these algebras arose from our research on the homologica...

the the main objective of this research paper is to present 3-d elasticity solution for free vibration analysis of elastically supported continuously graded carbon nanotube-reinforced (cgcntr) annular plates. the volume fractions of oriented, straight single-walled carbon nanotubes (swcnts) are assumed to be graded in the thickness direction. an equivalent continuum model based on the eshelby-m...

abstract. let (r,p) be a noetherian unique factorization do-main (ufd) and m be a finitely generated r-module. let i(m)be the first nonzero fitting ideal of m and the order of m, denotedord_r(m), be the largest integer n such that i(m) ⊆ p^n. in thispaper, we show that if m is a module of order one, then either mis isomorphic with direct sum of a free module and a cyclic moduleor m is isomorphi...

In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial ideals are lattice-linear and thus their minimal resolution can be constructed as a poset resolution. We then use this result to give a description of the m...

Under reasonable assumptions, a group action on module extends to the minimal free resolutions of module. Explicit descriptions these actions can lead better understanding by providing, for example, convenient expressions their differentials or alternative characterizations Betti numbers. This article introduces an algorithm computing characters finite groups acting finitely generated graded mo...

If M is the complement of a hyperplane arrangement, and A = H(M, k) is the cohomology ring of M over a field of characteristic 0, then the ranks, φk, of the lower central series quotients of π1(M) can be computed from the Betti numbers, bii = dimTor A i (k, k)i, of the linear strand in a minimal free resolution of k over A. We use the Cartan-Eilenberg change of rings spectral sequence to relate...

Let R = k[x 1 ,. .. , xn] and let I be the ideal of n + 1 generically chosen forms of degrees d 1 ≤ · · · ≤ d n+1. We give the precise graded Betti numbers of R/I in the following cases: • n = 3; • n = 4 and 5 i=1 d i is even; • n = 4, 5 i=1 d i is odd and d 2 + d 3 + d 4 < d 1 + d 5 + 4; • n is even and all generators have the same degree, a, which is even; • (n+1 i=1 d i) − n is even and d 2 ...

We prove a reformulation of the multiplicity upper bound conjecture and use that reformulation to prove it for three-dimensional simplicial complexes and homology manifolds with many vertices. We provide necessary conditions for a Cohen-Macaulay complex with many vertices to have a pure minimal free resolution and a characterization of flag complexes whose minimal free resolution is pure.