$(\alpha, 1)$ DERIVATIONS ON SEMIRINGS

On generalized left (alpha, beta)-derivations in rings

Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...

on generalized left (alpha, beta)-derivations in rings

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

Orderings on semirings

Though more general definitions are sometimes used, for this paper a semiring will be defined to be a set S with two operations + (addition) and 9 (multiplication); with respect to addition, S is a commutative monoid with 0 as its identity dement 9 With respect to multiplication, S is a (generaily noncommutat ive) monoid with 1 as its identity element. Connecting the two algebraic structures ar...

On * – k - semirings

A *–k-semiring is an ordered semiring S equipped with a star operation such that for any a,b 2 S, a*b is the least fixed point of the linear mapping x # ax + b over S. The notion of *–k-semirings is a generalization of several important concepts such as continuous semirings, (weak) inductive *-semirings and the Kleene algebras of Conway and Kozen. We investigate several basic properties of *–k-...

1 Semirings and formal power series