Abstract We build on the description of left congruences an inverse semigroup in terms kernel and trace due to Petrich Rankin. The notion for a congruence is developed. Various properties are discussed, particular that full subsemigroup both maps onto $$\cap $$ ? -homomorphisms. It shown determined by its ker...

We present the following reflexivity-like result concerning the automorphism group of the C∗-algebra B(H), H being a separable Hilbert space. Let φ : B(H) → B(H) be a multiplicative map (no linearity or continuity is assumed) which can be approximated at every point by automorphisms of B(H) (these automorphisms may, of course, depend on the point) in the operator norm. Then φ is an automorphism...

Pairings are particular bilinear maps, and as any bilinear maps they factor through the tensor product as group homomorphisms. Besides, nothing seems to prevent us to construct pairings on other abelian groups than elliptic curves or more general abelian varieties. The point of view adopted in this contribution is based on these two observations. Thus we present an elliptic curve free study of ...

Let $${{\mathfrak {A}}}\, $$ and '$$ be two $$C^*$$ -algebras with identities $$I_{{{\mathfrak }$$ '}$$ , respectively, $$P_1$$ $$P_2 = I_{{{\mathfrak } - P_1$$ nontrivial projections in . In this paper, we study the characterization of multiplicative $$*$$ -Lie–Jordan-type maps, where notion these maps arise here. particular, if $${\mathcal {M}}_{{{\mathfrak is a von Neumann algebra relative $...

In this paper, we further develop the study of rings integro-differential-delay operators considered as noncommutative polynomial algebras satisfying standard calculus identities. Within algebraic analysis approach, show that transformations and reductions linear differential time-delay systems can be interpreted homomorphisms isomorphisms finitely presented left modules over an algebra operato...

This paper presents a method to find new de Bruijn cycles based on ones of lesser order. This is done by mapping a de Bruijn cycle to several vertex disjoint cycles in a de Bruijn digraph of higher order and connecting these cycles into one full cycle. We characterize homomorphisms between de Bruijn digraphs of different orders that allow this construction. These maps generalize the well-known ...

This paper is devoted to giving the theoretical background for an algorithm for computing homomorphisms induced by maps in homology. The principal idea is to insert the graph of a given continuous map f into a graph of a multi-valued representable map F . The multi-valued representable maps have well developed continuity properties and admit a finite coding that permits treating them by combina...

In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. We extend it to pairs (f1, f2) of maps between manifolds of arbitrary dimensions, using nonstabilized normal bordism theory as our main tool. This leads to estimates of the minimum numbers MCC(f1, f2) (and MC(f1, f2), resp.) of pathcomponents (and of points, resp.) in the coinciden...

We claim that monomorphisms in Sets and Groups are the usual injective maps and homomorphisms. First, suppose that f : A → B is a set injection and that fg = gh. Then for all c ∈ C, we have f(g(c)) = f(h(c)) implies g(c) = h(c) by injectivitiy. Hence g = h. Conversely, suppose f : A → B is not an injection. Then let f(a) = f(a′) for some a 6= a′ ∈ A. Then let g(c) = a and h(c) = a′ for all c ∈ ...

We have already met covering spaces in Chapter 2, where our discussion was geometric and basically limited to definitions and examples. In this chapter, we return to this topic from a more algebraic point of view, which will allow us to produce numerous examples coming from group actions and to classify all covering spaces with given base (provided the latter is “nice” enough). The main tools w...