Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

Let τ be a hereditary torsion theory on ModR and suppose that Qτ : ModR → ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ : M →M is the colocalization functor, the...

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.

Model checking of recursion schemes, known as higher-order model checking, has actively been studied recently and is becoming a basis for verification of higher-order programs. Some practical model checking algorithms have been developed based on the reduction from model checking to intersection type inference, but they are not completely satisfactory. We propose a novel approach to developing ...

We extend an existing first-order typing system for strictness analysis to the fully higher-order case, covering both the derivation system and the inference algorithm. The resulting strictness typing system has expressive capabilities far beyond that of traditional strictness analysis systems. This extension is developed with the explicit aim of formally proving soundness of higher-order stric...

This paper discusses implementations of distributed garbage collectors derived using a previously developed methodology which involves mappings of distributed termination detection algorithms (DTAs) to local garbage collection schemes. Implementations produced by such mappings preserve the safety and completeness properties of the original local collectors. Through our collector implementations...

Suppose that we are given a surface S over a finite field of characteristic p, a curve C ⊂ S , and a point x ∈ C such that both S and C are regular at x. Then one can attach to these data the quotient field of the completion ̂ (ÔS,x)C of the localization at C of the completion ÔS,x of the local ring OS,x of S at x. This is a two-dimensional local field over a finite field, i.e., a complete discr...

Local fixpoint iteration describes a technique that restricts in function spaces to needed arguments only. It has been studied well for first-order functions abstract interpretation and also model checking. Here we consider the problem least greatest fixpoints of arbitrary type order. We define an algebra simply-typed higher-order with order express evaluation problems as they occur routinely v...

Let R be a prime ring with a right generalized (α, β)derivation f and let a ∈ R. Suppose that af(x)n = 0 for all x ∈ R, where n is a fixed positive integer. Then af(x) = 0 for all x ∈R. In particular, if f is either a regular right generalized (α, β)-derivation or a nonzero generalized (α, β)-derivation, then a = 0. In [13] I. N. Herstein proved that if R is a prime ring and d is an inner deriv...

This article investigates local properties of the further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M from viewpoint of study of submanifold quantum mechanics. We show that kernel of a certain Dirac operator defined over S, which we called submanifold Dirac operator, gives the data of the immersion. In the derivation, the simple Frobe...