The set of all (n×n) non-singular matrices over the field F. And this forms a group under operation matrix multiplication. This is called general linear dimension F, denoted by . determinant these homomorphism from into F* and kernel was special Thus subgroup which contains one. rationally valued characters rational representations are written as combination induced for groups discussed in pape...

We study a cross-ratio of four generic points of S which comes from spherical CR geometry. We construct a homomorphism from a certain group generated by generic configurations of four points in S to the pre-Bloch group P(C). If M is a 3-dimensional spherical CR manifold with a CR triangulation, by our homomorphism, we get a P(C)-valued invariant for M . We show that when applying to it the Bloc...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

We study the quantum ( $$C^*$$ ) convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, -extreme POVMs countable spaces (in particular for finite sets) are always spectral (normalized projection measures). More generally shown atomic spectral. A Krein–Milman type theorem ha...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

In a valued constraint satisfaction problem (VCSP), the goal is to find an assignment of labels to variables that minimizes a given sum of functions. Each function in the sum depends on a subset of variables, takes values which are rational numbers or infinity, and is chosen from a fixed finite set of functions called a constraint language. The case when all functions take only values 0 and inf...

We give a presentation of the construction of motivic integration, that is, a homomorphism between Grothendieck semigroups that are associated with a first-order theory of algebraically closed valued fields, in the fundamental work of Hrushovski and Kazhdan [12]. We limit our attention to a simple major subclass of V -minimal theories of the form ACVF S , that is, the theory of algebraically cl...

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...