Let k be a field, G an abelian group with a bicharacter, A a colour algebra; i.e., an associative graded k-algebra with identity, C a graded A-coring that is projective as a right A-module, C∗ the graded dual ring of C and Λ a left graded C-comodule that is finitely generated as a graded right C∗-module. We give necessary and sufficient conditions for projectivity and flatness of a graded modul...

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...

We describe a scalable and unified architecture for a Montgomery multiplication module which operates in both types of finite fields GF (p) and GF (2). The unified architecture requires only slightly more area than that of the multiplier architecture for the field GF (p). The multiplier is scalable, which means that a fixed-area multiplication module can handle operands of any size, and also, t...

The category of totally ordered graded module braids and that of the exact interlocking sequences are shown to be equivalent. As an application of this equivalence, we show the existence of a connection matrix for a totally ordered graded module braid without assuming the existence of chain complex braid that induces the given graded module braid.

We show that each direct summand of the associated graded module test filtration τ(M,fλ)λ≥0 admits a natural Cartier structure. If λ is an F-jumping number, then this structure nilpotent on τ(M,fλ−ε)/τ(M,fλ) if and only denominator divisible by p. also these structures coincide with certain are obtained considering D-modules to M were used construct Bernstein-Sato polynomials. Moreover, we poin...

In this paper, we consider the classification of irreducible Zand Z2-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight irreducible modules. As a consequence, we also determine all the modules with nonz...

Given a module M over a ring R that has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology H I(M) at any graded ideal I in terms of Ext modules. We use this method to obtain finiteness results for the local cohomology of graded modules over semigroup rings. In particular we prove that for a semigroup Q whose saturation Q is simplicial, and a finitely g...

Let p ≥ 3 be a prime. We consider the cyclotomic extension Z(p)[ζp2] of Z(p), with Galois group G := (Z/p2)∗. Since this extension is wildly ramified, Z(p)[ζp2] is not projective as a module over the group ring Z(p)G (Speiser). Extending this module structure, we can regard Z(p)[ζp2 ] as a module over the twisted group ring Z(p)[ζp2] ≀G; as such, it remains faithful and non projective. We calcu...

We establish a relationship between the graded quotients of a filtered holonomic D-module, their sheaf-theoretic duals, and the characteristic variety, in case the filtered D-module underlies a polarized Hodge module on a smooth algebraic variety. The proof is based on Saito’s result that the associated graded module is Cohen-Macaulay, and on local duality on the cotangent bundle.