Let G be a group with identity e. R G-graded commutative ring and M graded R-module. We introduce the concept of Ie-prime submodule as generalization prime for I =?g?G Ig fixed ideal R. give number results concerning this class submodules their homogeneous components. A proper N is said to if whenever rg ? h(R) mh h(M) rgmh IeN, then either (N :R M) or N.

This work concerns finite free complexes with length homology over a commutative noetherian local ring $R$. The focus is on that have $\mathrm{dim}\, R$, which the smallest possible value, and in particular resolutions of modules projective dimension. Lower bounds are obtained Euler characteristic such short when $R$ strict complete intersection, also Dutta multiplicity, localization at its max...

The conjectures of M. Boij and J. Söderberg [3], proven by D. Eisenbud and F.-O. Schreyer [8] (see also [7, 4]), link the extremal properties of invariants of graded free resolutions of finitely generated modules over the polynomial ring S = k[x1, . . . , xn] with the Herzog–Huneke–Srinivasan Multiplicity Conjectures. Here k is any field and S has the standard Z-grading. In the course of their ...

We consider an action of the automorphism group Aut(F n ) free F rank on filtered vector space A d (n) Jacobi diagrams degree oriented arcs. This induces associated graded (n), which is identified with B open diagrams, general linear GL(n,?) and Lie algebra IA-automorphism its lower central series. use these actions to study )-module structure (n). In particular, we case where d=2 in detail giv...

We study the transfer of (dual) relative CS-Rickart properties via functors between abelian categories. consider fully faithful as well adjoint pairs functors. give several applications to Grothendieck categories and, in particular, (graded) module and comodule