Derivations on Pseudoquotients
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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.
KeywordsEquivalence Class Generalize Derivation Algebra Homomorphism Invertible Element Commutative Semigroup
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- 2.Li Jiankui and Jiren Zhou, “Characterization of Jordan derivations and Jordan homomorphisms,” Linear and Multilinear Algebra, 52, No. 2, 193–204 (2011).Google Scholar