Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V G-modules which occur as submodules of irreducible V -modules by using intertwining operators for V . We also determine some fusion rules for a vertex operator algebra as an application.

Let [Formula: see text] be a commutative Noetherian ring. For finitely generated text]-module text], Northcott introduced the reducibility index of which is number submodules appearing in an irredundant irreducible decomposition submodule text]. On other hand, for Artinian Macdonald proved that sum-irreducible representation does not depend on choice representation. This called sum-reducibility...

Let a be an ideal of commutative Noetherian ring R with identity. We study finitely generated R-modules M whose a-finiteness and a-cohomological dimensions are equal. In particular, we examine relative analogues quasi-Buchsbaum, Buchsbaum surjective modules. reveal several interactions between these types modules that extend some the existing results in classical theory to one.

This paper applies G. Lyubeznik’s notion of F -finite modules to describe in a very down-to-earth manner certain annihilator submodules of some top local cohomology modules over Gorenstein rings. As a consequence we obtain an explicit description of the test ideal of Gorenstein rings in terms of ideals in a regular ring.

A method for solving CCS equations of type (AIX)\L ~ B, where X is unknown, is presented. The method is useful in a top-down design methodology: if a system (B) and some of its submodules (.4) axe specified, solving such an equation amounts to constructing the missing submodules. The method works by successively transforming equations into simpler equations, in parallel with generation of a sol...

The similarity submodules for various lattices and modules of interest in the crystal and quasicrystal theory are determined and the corresponding semigroups, along with their zeta functions, are investigated. One application is to the colouring of crystals and quasicrystals.

Let (R,m) be a commutative Noetherian local ring with m = (0). We give a condition for R to have a non-free module of G-dimension zero. We shall also construct a family of non-isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of projective space. We shall finally show that the subcategory consisting of modules of G-dimension zero over R is not necessarily a...

We completely describe the decompositions (into indecomposable submodules) of the tensor products of irreducible sl(2)-modules in characteristic 3. The answer resembles analogous decompositions for the Lie superalgebra sl(1|1).

This is an exposition of Goldie’s theorem with a section on Ore localization and with an application to defining ranks for finitely generated modules over non–commutative noetherian rings.