Derived dualities induced by a 1-cotilting bimodule

Rep#1: Deformations of a bimodule algebra

Definition 3. Let B be a ring. Then, we denote by B [[t]] the ring of formal power series over B in the indeterminate t, where t is supposed to commute with every element of B. Formally, this means that we define B [[t]] as the ring of all sequences (b0, b1, b2, ...) ∈ BN (where N means the set {0, 1, 2, ...}), with addition defined by (b0, b1, b2, ...) + (b ′ 0, b ′ 1, b ′ 2, ...) = (b0 + b ′ ...

On a Finitistic Cotilting-type Duality

Let R and S be arbitrary associative rings. Given a bimodule RWS , we denote by ∆? and Γ? the functors Hom?(−, W ) and Ext?(−, W ), where ? = R or S. We say that RWS is a finitistic weakly cotilting bimodule (briefly FWC) if for each module M cogenerated by W , finitely generated or homomorphic image of a finite direct sum of copies of W , ΓM = 0 = Ext(M, W ). We are able to describe, on a larg...

Dualities and Equivalences Induced by Adjoint Functors

Dualities Between Nets and Automata Induced by Schizophrenic Objects

The so-called synthesis problem for nets, which consists in deciding whether a given graph is isomorphic to the case graph of some net, and then constructing the net, has been solved in the litterature for various types of nets, ranging from elementary nets to Petri nets. The common principle for the synthesis is the idea of regions in graphs, representing possible extensions of places in nets....

Warfield Dualities Induced by Self-small Mixed Groups

For a self-small abelian group A of torsion-free rank 1, we characterize A-reflexive abelian groups which are induced by the contravariant functor Hom(−, A) in two cases: the range of Hom(−, A) is the category of all abelian groups, respectively the range of Hom(−, A) is the category of all left E-modules, where E is the endomorphism ring of A.