The structure of the group Aut(Cn) of biholomorphisms of Cn is largely unknown if n > 1. In stark contrast Aut(C) is rather small, consisting of the nonconstant affine linear maps. The description of Aut(C) follows from the observation that an injective holomorphic function f : C → C satisfying f(0) = 0 and f ′(0) = 1 must be the identity. These considerations suggest that similar characterizat...

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of length three. An injective edge coloring of a graph G = (V,E) is a coloring c of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then c(e1) 6= c(e3). The injective edge coloring number χ ′ i(G) is the minimum number of colors permitted in such a coloring. In this paper,...

The isomorphism problem is not known to be NP-complete nor polynomial. Yet it is crucial when maintaining large conceptual graphs databases. Taking advantage of conceptual graphs speciicities, whenever, by means of structural functions, a linear order of the conceptual nodes of a conceptual graph G can be computed as invariant under automorphism, a descriptor is assigned to G in such a way that...

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

Let $R$ be a ring, $n$ an non-negative integer and $d$ positive or $\infty$. A right $R$-module $M$ is called \emph{$(n,d)^*$-projective} if ${\rm Ext}^1_R(M, C)=0$ for every $n$-copresented $C$ of injective dimension $\leq d$; ring \emph{right $(n,d)$-cocoherent} with $id(C)\leq d$ $(n+1)$-copresented; $(n,d)$-cosemihereditary} whenever $0\rightarrow C\rightarrow E\rightarrow A\rightarrow 0$ e...