This paper produces a recursive formula of the Betti numbers of certain Stanley-Reisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projectiveâ€¦ (More)

of R/I, in which R(âˆ’j) denotes the graded free module obtained by shifting the degrees of elements in R by j. The numbers Î²ij , which we shall refer to as the ith Betti numbers of degree j of R/I,â€¦ (More)

Let (R, m) be a local Noetherian ring, let I âŠ‚ R be any ideal and let M be a finitely generated R-module. It has been long conjectured that the local cohomology modules H I(M) have finitely manyâ€¦ (More)

The aim of this paper is to provide a description of parameter test ideals of local CohenMacaulay rings of prime characteristic p. The nature of this description will be such that it will allow us toâ€¦ (More)

This paper is concerned with ideals in a commutative Noetherian ring R of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of R generated by regularâ€¦ (More)

In [HY] Hara and Yoshida defined the notion of generalized test ideals Ï„(a) âŠ† R for ideals a of regular local rings R and non-negative parameters c âˆˆ R. Since then several papers studied theâ€¦ (More)