We prove that over a commutative noetherian ring the three approaches to introducing depth for complexes: via Koszul homology, via Ext modules, and via local cohomology, all yield the same invariant. Using this result, we establish a far reaching generalization of the classical AuslanderBuchsbaum formula for the depth of finitely generated modules of finite projective dimension. We extend also ...

A p-indigent module is one that subprojective only to projective modules. An RD-projective any torsionfree (and flat) module. $T$ called rdp-indigent if it In this work, we consider the structure of SRDP rings whose (simple) right $R$-modules are or torsionfree. Moreover, new characterizations P-coherent and presented by subprojectivity domains.

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...

In automated synthesis, given a specification, we automatically create a system that is guaranteed to satisfy the specification. In the classical temporal synthesis algorithms, one usually creates a “flat” system “from scratch”. However, real-life software and hardware systems are usually created using preexisting libraries of reusable components, and are not “flat” since repeated subsystems ar...

The purpose of this paper is to give a constructive algorithm for the computation of bases of finitely presented free modules over the Weyl algebras of differential operators with polynomial or rational coefficients. In particular, we show how to use these results in order to recognize when a multidimensional linear system defined by partial differential equations with polynomial or rational co...

In automated synthesis, given a specification, we automatically create a system that is guaranteed to satisfy the specification. In the classical temporal synthesis algorithms, one usually creates a “flat” system “from scratch”. However, real-life software and hardware systems are usually created using preexisting libraries of reusable components, and are not “flat” since repeated sub-systems a...

Let M be a complete nonsingular fine moduli space of modules over an algebra S. A set of conditions is given for the Chow ring of M to be generated by the Chern classes of certain universal bundles occurring in a projective resolution of the universal S-module on M . This result is then applied to the varieties GT parametrizing homogeneous ideals of k[x, y] of Hilbert function T , to moduli spa...