We consider the problem of deciding the security of cryptographic protocols for a bounded number of sessions, taking into account some algebraic properties of the security primitives, for instance Abelian group properties. We propose a general method for deriving decision algorithms, splitting the task into 4 properties of the rewriting system describing the intruder capabilities: locality, con...

in this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a banach algebra $a$ into a semisimple banach algebra $b$ is continuous.

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

We present an undecidability result for the verification of security protocols. Since the perfect cryptography assumption is unrealistic for cryptographic primitives with visible algebraic properties, several recent works relax this assumption, allowing the intruder to exploit these properties. We are interested in the Abelian groups theory in combination with the homomorphism axiom. We show th...

Let φ : (R, m)→ (S, n) be a local homomorphism of commutative noetherian local rings. Suppose that M is a finitely generated S-module. A generalization of Grothendieck’s non-vanishing theorem is proved for M (i.e. the Krull dimension of M over R is the greatest integer i for which the ith local cohomology module of M with respect to m, Hi m(M), is non-zero). It is also proved that the Gorenstei...

Kalicki showed in [5] that both of these problems are decidable. Kalicki’s algorithm is obtained by using a fact that only a bounded number of identities has to be verified to decide whether a finite algebra belongs to a finitely generated variety. This approach to the problem turned out to be very inefficient. Bergman and Slutzki presented in [2] an algorithm that solves the universal membersh...

Let A be a supersingular abelian variety deened over a nite eld k. We give an approximate description of the structure of the group A(k) of k-rational points of A in terms of the characteristic polynomial f of the Frobenius endomorphism of A relative to k. Write f = Q gi e i for distinct monic irreducible polynomials gi and positive integers ei, we show that there is a group homomorphism ' : A(...

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

This paper continues the investigation of the rst author begun in part one. The hereditary properties of n-homomorphism amenability for Banach algebras are investigated and the relations between n-homomorphism amenability of a Banach algebra and its ideals are found. Analogous to the character amenability, it is shown that the tensor product of two unital Banach algebras is n-homomorphism amena...

Recall that a continuous function $fcolon Xto Y$ between Tychonoff spaces is proper if and only if the Stone extension $f^{beta}colon beta Xtobeta Y$ takes remainder to remainder, in the sense that $f^{beta}[beta X-X]subseteq beta Y-Y$. We introduce the notion of ``taking remainder to remainder" to frames, and, using it, we define a frame homomorphism $hcolon Lto M$ to be $beta$-proper, $lambd...