We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure. Let X be a finite space and Y be a compact space. Then the space F (X,Y ) of all maps from X to Y , is a compact space with compact-open topology. The notion of quantum family of all maps, defined by Woronowicz [8] and Soltan [5], is a no...

We show that for every sofic chunk $E$ there is a bijective homomorphism $f: E_c \rightarrow E$, where $E_c$ of the group computable permutations $\mathbb{N}$ so approximating morphisms can be viewed as restrictions to finite subsets $\mathbb{N}$. Using this we study some relevant effectivity conditions associated with chunks and their profiles.

We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [AAD04] and models introduced and studied by Mazurkiewicz [Maz04a,Maz04b]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labell...

The transfer homomorphism from a group G to an abelian subgroup H of finite index in G arises from the natural action of G on the cosets of H. It plays an important role in the study of unsolvable groups and aids in the characterization of groups in which all Sylow p-subgroups are cyclic. In this paper, we will define the transfer homomorphism, and then investigate a few of its properties. Let ...

‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...

An n-valued multimap is a continuous multivalued function φ : X ⊸ Y such that φ(x) is an unordered subset of n points of Y for each x ∈ X. If X and Y are finite polyhedra, then φ induces a graded homomorphism of homology with rational coefficients. For φ : X ⊸ X the Lefschetz number L(φ) of φ is defined to be the Lefschetz number of the induced homomorphism. If L(φ) 6= 0, then every n-valued mu...

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...

Let Fn be a free group of rank n and F n the quotient group of Fn by the subgroup [Γn(3),Γn(3)][[Γn(2),Γn(2)],Γn(2)] where Γn(k) denotes the k-th subgroup of the lower central series of the free group Fn. In this paper, we determine the group structure of the graded quotients of the lower central series of the group F n by using a generalized Chen’s integration in free groups. Then we apply it ...