Related papers: Primary decomposition of modules: a computational …

We introduce the notion of multiplication kernels of birational and $D$-module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its…

The purpose of this paper is to introduce basic concepts that are fundamental in the examination of composite moduli, while avoiding the notoriously difficult problem of prime-factorization. We introduce a new class of numbers, called…

Let $R$ be a finite ring and let $M, N$ be two finite left $R$-modules. We present two distinct deterministic algorithms that decide in polynomial time whether or not $M$ and $N$ are isomorphic, and if they are, exhibit an isomorphism. As…

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…

Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

The theme of this paper is to `solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field $K$. Representations of semi-simple Lie algebras and…

For modular indecomposable representations of a cyclic group $G$ of prime order $p$ we propose a list of polynomial invariants of degree $\leq 3$ that, together with a simple invariant of degree $p$, separate generic orbits and generate the…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith…

The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…

In this article, we generalize the concept of torsion pairs and study its structure. As a trial of obtaining all torsion pairs, we decompose torsion pairs by projective modules and injective modules. Then we calculate torsion pairs on the…

An algorithm is described to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for modules that are constructed as a submodule of a…

The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is…

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…

A direct sum decomposition theory is developed for direct summands (and complements) of modules over a semiring $R$, having the property that $v+w = 0$ implies $v = 0$ and $w = 0$. Although this never occurs when $R$ is a ring, it always…

Composition is an important feature of a specification language, as it enables the design of a complex system in terms of a product of its parts. Decomposition is equally important in order to reason about structural properties of a system.…