Let R be a ring and let B be a commutative ring. Let p : R −→ B be a homogeneous multiplicative polynomial law of degree n. The main result of this paper is to show that p is essentially a determinant, in the sense that p is obtained from a determinant by left and right composition with ring homomorphisms. This is achieved using results on the invariants of matrices in positive characteristic d...

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...

T he essence of harmonic analysis is to decompose complicated expressions into pieces that reflect the structure of a group action when there is one. The goal is to make some difficult analysis manageable. In the seventeenth and eighteenth centuries, the groups that arose in this connection were the circle R/2πZ , the line R , and finite abelian groups. Embedded in applications were decompositi...

We prove that Jordan triple elementary surjective maps on unital rings containing a nontrivial idempotent are automatically additive. The first result about the additivity of maps on rings was given by Martindale III in an excellent paper [7]. He established a condition on a ring R such that every multiplicative bijective map on R is additive. More precisely, he proved the following theorem. Th...

There are many instances of the principle that if A is an algebra of functions on X, then every ring homomorphism A → C is given by evaluation at a particular x ∈ X. Examples are the nullstellensatz in algebraic geometry and the result of Gelfand when X is a compact Hausdorff space. In these cases one can regard X as being included in Hom(A, C) as the set of those f : A → C which satisfy the se...

This paper approaches the problem of image denoising from an Independent Component Analysis (ICA) perspective. Considering that the pixels intensity constituting the crude images represents the useful signal corrupted with noise, we show that, a nonlinear ICA-based approach can provide a satisfactory solution to the NonLinear Blind Source Separation problem (NLBSS). SelfOrganizing Maps (SOMs) a...

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

This paper is a survey of several results concerning finite dualities, a special case of the famous Constraint Satisfaction Problem (CSP). In CSP, the point is to characterize a class C of objects X determined by constraints represented by the requirement of the existence of structure preserving mappings from X into special ones. In a finite duality, such a class C is characterized by the non-e...