Derivations on Pseudoquotients
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 homomor...
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| Datum: | 2013 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2013
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2472 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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