Let A and B be unital rings. An additive map T:A→B is called a weighted Jordan homomorphism if c=T(1) an invertible central element cT(x2)=T(x)2 for all x∈A. We provide assumptions, which are in particular fulfilled when A=B=Mn(R) with n≥2 R any ring 12, under every surjective the property that T(x)T(y)+T(y)T(x)=0 whenever xy = yx 0 homomorphism. Further, we show prime char(A)≠2,3,5, then bijec...

The problem of finding hidden state in a POMDP and the problem of finding abstractions for MDPs are closely related. In this paper, we analyze the connection between existing Predictive State Representation methods [3] and homomorphic reductions of Markov Processes [5, 6]. We formally define a POMDP homomorphism, then extend PSR reduction methods to find POMDP homomorphisms when the original PO...

Abstract For given Boolean algebras $\mathbb {A}$ and {B}$ we endow the space $\mathcal {H}(\mathbb {A},\mathbb {B})$ of all homomorphisms from to with various topologies study convergence properties sequences in . We are particular interested situation when is a measure algebra as this case obtain natural tool for studying topological ultrafilters on random extensions set-theoretical universe....

A graph homomorphism from a graph G to a graph H is a mapping h : V (G)→ V (H) such that h(u) ∼ h(v) if u ∼ v. Graph homomorphisms are well studied objects and, for suitable choices of eitherG orH, many classical graph properties can be formulated in terms of homomorphisms. For example the question of wether there exists a homomorphism from G to H = Kq is the same as asking wether G is q-colour...

We present sufficient conditions under which effective descent morphisms in a quasivariety of universal algebras are the same as regular epimorphisms and examples for which they are the same as regular epimorphisms satisfying projectivity. 1. Preliminaries A variety is a full subcategory of the category of structures for a first order (one sorted) language, closed under substructures, products ...

In this paper, we consider certain descending filtrations of the $\mathrm{SL}(m,\C)$-representation algebras free groups and abelian groups. By using it, introduce analogs Johnson homomorphisms automorphism We show that first are extended to as crossed homomorphisms. Furthermore induce Kawazumi's cocycles Morita's cocycles. This works generalization our previous results for $\mathrm{SL}(2,\C)$-...

The notion of graph covers is a discretization covering spaces introduced and deeply studied in topology. In discrete mathematics theoretical computer science, they have attained lot attention from both the structural complexity perspectives. Nonetheless, disconnected graphs were usually omitted considerations with explanation that it sufficient to understand coverings connected components targ...