We give a purely combinatorial characterization of complete Stanley–Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.

This paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of ...

This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra

We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Z(s) and in terms of relative volumes of lattice ...

Let $G_n$ be a double cover of either the alternating group $A_n$ or the symmetric group $S_n$, and let $G_{n-1}$ be the corresponding double cover of $A_{n-1}$ or $S_{n-1}$. For every odd $n\geq 3$ and every field $k$ of ...

Let R be a Noetherian ring. We prove that R has global dimension at most two if, and only if, every prime ideal of R is of linear type. Similarly, we show that R has global dimension at most three if, and only if, every ...

Let p be a prime number. Let C p , the cyclic group of order p , permute transitively a set of indeterminates f x 1 ;:::;x p g . We prove that the invariant eld Q ( x 1 ;:::;x p ) C p is rational over Q if and only if the ( p

We prove the rationality of the Poincaré series of multiplier ideals in any dimension thus extending the main results for surfaces of Galindo and Monserrat and Alberich-Carramiñana et al. Our results also hold for Poincaré ...

For a given ideal I of a commutative ring ç A,B = A/I, the vanishing of the second André-Quillen (co)homology functor H2(A,B,*) is characterized in terms of the canonical homomorphism a:S(I)->R(I) from the symmetric algebra ...