Derivations on Pseudoquotients

  • A. Majeed
  • P. Mikusiński

Abstract

A space of pseudoquotients denoted by B(X, S) is defined as equivalence classes of pairs (x, f); where x is an element of a nonempty set X, f is an element of S; a commutative semigroup of injective maps from X to X; and (x, f) ~ (y, g) for gx = fy: If X is a ring and elements of S are ring homomorphisms, then B(X, S) is a ring. We show that, under natural conditions, a derivation on X has a unique extension to a derivation on B(X, S): We also consider (α, β) -Jordan derivations, inner derivations, and generalized derivations.
Published
25.06.2013
How to Cite
MajeedA., and MikusińskiP. “Derivations on Pseudoquotients”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 6, June 2013, pp. 863–869, http://umj.imath.kiev.ua/index.php/umj/article/view/2472.
Section
Short communications