Let R be a prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R. An additive map D: R → R is called an α-derivation (or a skew derivation) on R if D(xy) = D(x)y + α(x)D(y) for all x, y \in R. An additive mapping F: R → R is called a generalized α-derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F(xy) = F(x)y + α(x)D(y) for all x, y \in R. We prove that, if F is a nonzero generalized skew derivation of R such that F(x)×[F(x), x]n = 0 for any x \in L, then either there exists λ \in C such that F(x) = λx for all x \in R, or R\subset M_{2}\left ( C \right ) and there exist a \in Qr and λ \in C such that F(x) = ax + xa + λx for any x \in R., Vincenzo De Filippis., and Obsahuje seznam literatury
We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra $\mathcal A$. We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice $\mathcal D (A)$ of all deductive systems on $\mathcal A$. Moreover, relative annihilators of $C\in \mathcal D (A)$ with respect to $B \in \mathcal D (A)$ are introduced and serve as relative pseudocomplements of $C$ w.r.t. $B$ in $\mathcal D (A)$.
The concepts of an annihilator and a relative annihilator in an autometrized $l$-algebra are introduced. It is shown that every relative annihilator in a normal autometrized $l$-algebra $\mathcal {A}$ is an ideal of $\mathcal {A}$ and every principal ideal of $\mathcal {A}$ is an annihilator of $\mathcal {A}$. The set of all annihilators of $\mathcal {A}$ forms a complete lattice. The concept of an $I$-polar is introduced for every ideal $I$ of $\mathcal {A}$. The set of all $I$-polars is a complete lattice which becomes a two-element chain provided $I$ is prime. The $I$-polars are characterized as pseudocomplements in the lattice of all ideals of $\mathcal {A}$ containing $I$.
The aim of this paper is to show relationships between the different formalism for uncertainty in artificial intelligence and its applications. We introduce a model of fuzzy logic programming (FLP). We propose a solution to the problem of discontinuous restricted semantics of annotated logic programs introducing annotated logic programs with left continuous annotation terms (ALPLCA). We show that FLP and ALPLCA have the same expressive power and both háve continuous semantics. We have soundness and completeness results. This enables us to introduce a new relational algebra. Our procedural semantics enables us to estimate the truth values of answers during the computation. Using this, we introduce several search strategies. Consequences of many valued-logic abduction and many-valued resolutions are also discussed.