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Ukrainian Mathematical Journal

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

Derivations on Pseudoquotients

  • A. Majeed
  • P. Mikusiński
Article
  • 47 Downloads

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.

Keywords

Equivalence Class Generalize Derivation Algebra Homomorphism Invertible Element Commutative Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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