Pretty cleanness and filter-regular sequences

Filter-regular Sequences and Mixed Multiplicities

Let S be a finitely generated standard multigraded algebra over an Artinian local ring A; M a finitely generated multigraded S-module. This paper answers to the question when mixed multiplicities of M are positive and characterizes them in terms of lengths of A-modules. As an application, we get interesting results on mixed multiplicities of ideals, and recover some early results in [Te] and [TV].

Note on regular and coregular sequences

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

Stanley Decompositions, Pretty Clean Filtrations and Reductions modulo Regular Elements

We study the behavior of Stanley decompositions and of pretty clean filtrations under reduction modulo a regular element.

Discriminators and k-Regular Sequences

The discriminator of an integer sequence s = (s(i))i≥0, introduced by Arnold, Benkoski, and McCabe in 1985, is the map Ds(n) that sends n ≥ 1 to the least positive integer m such that the n numbers s(0), s(1), . . . , s(n − 1) are pairwise incongruent modulo m. In this note we consider the discriminators of a certain class of sequences, the k-regular sequences. We compute the discriminators of ...

Regular Sequences and Frequency Distributions