Ukrainian Mathematical Journal

, Volume 65, Issue 6, pp 959–966 | Cite as

Derivations on Pseudoquotients

  • A. Majeed
  • P. Mikusiński

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.


Equivalence Class Generalize Derivation Algebra Homomorphism Invertible Element Commutative Semigroup 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • A. Majeed
    • 1
  • P. Mikusiński
    • 1
  1. 1.CIITIslamabadPakistan

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