29 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
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
Duality Theorems for Crossed Products over Rings
In this note we extend duality theorems for crossed products obtained by M.
Koppinen and C. Chen from the case of a base field or a Dedekind domain to the
case of an arbitrary noetherian commutative ground ring under fairly weak
conditions. In particular we extend an improved version of the celebrated
Blattner-Montgomery duality theorem to the case of arbitrary noetherian ground
rings.Comment: 24 page