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...

During the last decades, structure of mod-2 cohomology Steenrod ring $\mathscr {A}$ became a major subject in Algebraic topology. One most direct attempt studying this by means modular representations general linear groups was surprising work [ Math. Z. 202 (1989), 493–523] William Singer, which introduced homomorphism, so-called algebraic transfer , mapping from coinvariants certain representa...

We study Gorenstein flat objects in the category Rep(Q,R) of representations a left rooted quiver Q with values Mod(R), all R-modules, where R is an arbitrary associative ring. show that representation X if and only for each vertex i canonical homomorphism φiX:⊕a:j→iX(j)→X(i) injective, R-modules X(i) CokerφiX are flat. As application, we obtain model structure on which give explicit descriptio...

Abstract We show that the image of a subshift X under various injective morphisms symbolic algebraic varieties over monoid universes with variety alphabets is finite type, respectively sofic subshift, if and only so . Similarly, let G be countable A , B Artinian modules ring. prove for every closed submodule $\Sigma \subset A^G$ -equivariant uniformly continuous module homomorphism $\tau \colon...

Sometimes the derivation is denoted by a→ a′. A ring equipped with a derivation is called a differential ring. The notions, differential subring, differential ring extension and homomorphism between differential rings, are clear. If (R, ∂) is a differential ring then the set of constants is by definition {r ∈ R : ∂(r) = 0}, and is easily seen to be a (differential) subring. ∂ means the k-fold i...

Time-Delay Interferometry (TDI) is the data processing technique that cancels large laser phase fluctuations affecting one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. By taking finite linear combinations of properly time-shifted measurements, are removed at any time $t$ and signals can be studied a requisite level precision. In this article we sh...

For any linear algebraic group G, we define a ring CHBG, the ring of characteristic classes with values in the Chow ring (that is, the ring of algebraic cycles modulo rational equivalence) for principal G-bundles over smooth algebraic varieties. We show that this coincides with the Chow ring of any quotient variety (V −S)/G in a suitable range of dimensions, where V is a representation of G and...

In this paper, we propose a new scheme based on ephemeral elliptic curves over finite ring with an RSA modulus. The is variant of both the and KMOV cryptosystems can be used for signature encryption. We study security show that it immune to factorization attacks, discrete-logarithm-problem sum-of-two-squares sum-of-four-squares isomorphism homomorphism attacks. Moreover, private exponents much ...

Let R be a ring and S a nonempty subset of R. Suppose that θ and φ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ,φ)-derivation (resp., Jordan left (θ,φ)derivation) on S if δ(xy) = θ(x)δ(y)+φ(y)δ(x) (resp., δ(x2) = θ(x)δ(x)+φ(x)δ(x)) holds for all x,y ∈ S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is show...