89 research outputs found
On Linear Difference Equations over Rings and Modules
In this note we develop a coalgebraic approach to the study of solutions of
linear difference equations over modules and rings. Some known results about
linearly recursive sequences over base fields are generalized to linearly
(bi)recursive (bi)sequences of modules over arbitrary commutative ground rings.Comment: 21 pages, to appear in IJMM
On the Linear Weak Topology and Dual Pairings over Rings
In this note we study the weak topology on paired modules over a (not
necessarily commutative) ground ring. Over QF rings we are able to recover most
of the well known properties of this topology in the case of commutative base
fields. The properties of the linear weak topology and the dense pairings are
then used to characterize pairings satisfying the so called -condition.Comment: 16 pages, to appear in "Topologu and its Applications
A Zariski Topology for Modules
Given a duo module over an associative (not necessarily commutative) ring
a Zariski topology is defined on the spectrum
of {\it fully prime} -submodules of . We
investigate, in particular, the interplay between the properties of this space
and the algebraic properties of the module under consideration.Comment: 22 pages; submitte
On Coreflexive Coalgebras and Comodules over Commutative Rings
In this note we study dual coalgebras of algebras over arbitrary (noetherian)
commutative rings. We present and study a generalized notion of coreflexive
comodules and use the results obtained for them to characterize the so called
coreflexive coalgebras. Our approach in this note is an algebraically
topological one.Comment: 39 page
Exact Sequences of Semimodules over Semirings
In this paper, we introduce and investigate a new notion of exact sequences
of semimodules over semirings relative to the canonical image factorization.
Several homological results are proved using the new notion of exactness
including some restricted versions of the Short Five Lemma and the Snake Lemma
opening the door for introducing and investigating homology objects in such
categories. Our results apply in particular to the variety of commutative
monoids extending results in homological varieties.Comment: arXiv admin note: substantial text overlap with arXiv:1111.033
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