Let A be an algebra, and let θ, φ be ring automorphisms of A. An additive mapping H : A → A is called a θ, φ -derivation if H xy H x θ y φ x H y for all x, y ∈ A. Moreover, an additive mapping F : A → A is said to be a generalized θ, φ -derivation if there exists a θ, φ derivation H : A → A such that F xy F x θ y φ x H y for all x, y ∈ A. In this paper, we investigate the superstability of gene...

Usual definitions of Dedekind domain are not well suited for an algorithmic treatment. Indeed, the notion of Noetherian rings is subtle from a constructive point of view, and to be able to get prime ideals involve strong hypotheses. For instance, if k is a field, even given explicitely, there is in general no method to factorize polynomials in k[X]. The work [2] analyses the notion of Dedekind ...

Abstract Let ℛ be a semiprime ring with unity e and ϕ , φ automorphisms of ℛ. In this paper it is shown that if satisfies 2

Tits has defined Kac–Moody and Steinberg groups over commutative rings, providing infinite dimensional analogues of the Chevalley–Demazure group schemes. Here we establish simple explicit presentations for all Steinberg and Kac–Moody groups whose Dynkin diagrams are hyperbolic and simply laced. Our presentations are analogues of the Curtis–Tits presentation of the finite groups of Lie type. Whe...

We present an algorithm that returns a proper factor of a polynomial Φ(x) over the p-adic integers Zp (if Φ(x) is reducible over Qp) or returns a power basis of the ring of integers of Qp[x]/Φ(x)Qp[x] (if Φ(x) is irreducible over Qp). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algo...

Let $$\underline{S}$$ be an arbitrary subset of $$R^n$$ where R is a domain with the field fractions $$\mathbb {K}$$ . Denote ring polynomials in n variables over by {K}[\underline{x}] $$ The integer-valued , denoted Int $$(\underline{S},R)$$ defined as set which maps to R. In this article, we study irreducibility for first time case when Unique Factorization Domain. We also show that our resul...

In the present paper, we study some notes on Berger type deformed Sasaki metric in cotangent bundle T∗MT∗M over an anti-paraKähler manifold (M,φ,g)(M,φ,g). We characterize geodesic properties for this metric. Next also construct almost anti-paraHermitian structures and search conditions these to be quasi-anti-paraKähler with respect