A Note on Multiplicative (Generalized) (α, β)-Derivations in Prime Rings
Let be a prime ring with center ). A map : → is called a multiplicative (generalized) ( , )-derivation if )= )+ ) is fulfilled for all ; ∈ , where : → is any map (not necessarily derivation) and ; : → are automorphisms. Suppose that and are two multiplicative (generalized) ( , )-derivations associat...
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| Veröffentlicht in: | Annales mathematicae Silesianae 2019-09, Vol.33 (1), p.266-275 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
be a prime ring with center
). A map
:
→
is called a multiplicative (generalized) (
,
)-derivation if
)=
)+
) is fulfilled for all
;
∈
, where
:
→
is any map (not necessarily derivation) and
;
:
→
are automorphisms. Suppose that
and
are two multiplicative (generalized) (
,
)-derivations associated with the mappings
and
, respectively, on
and
,
are automorphisms of
. The main objective of the present paper is to investigate the following algebraic identities: (
)
) +
) = 0, (
)
) +
) = 0, (
)
) +
) = 0, (
)
) =
) ○
) and (
)
) = [
),
)] for all
,
in an appropriate subset of |
|---|---|
| ISSN: | 0860-2107 2391-4238 |
| DOI: | 10.2478/amsil-2019-0008 |