On centrally-extended maps on rings
Let R be a ring with center Z . A map D of R (resp. T of R ) is called a centrally-extended derivation (resp. a centrally-extended endomorphism) if for each x , y ∈ R , D ( x + y ) - D ( x ) - D ( y ) ∈ Z and D ( x y ) - D ( x ) y - x D ( y ) ∈ Z (resp. T ( x + y ) - T ( x ) - T ( y ) ∈ Z and T ( x...
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| Published in | Beiträge zur Algebra und Geometrie Vol. 57; no. 1; pp. 129 - 136 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2016
|
| Subjects | |
| Online Access | Get full text |
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| Summary: | Let
R
be a ring with center
Z
. A map
D
of
R
(resp.
T
of
R
) is called a centrally-extended derivation (resp. a centrally-extended endomorphism) if for each
x
,
y
∈
R
,
D
(
x
+
y
)
-
D
(
x
)
-
D
(
y
)
∈
Z
and
D
(
x
y
)
-
D
(
x
)
y
-
x
D
(
y
)
∈
Z
(resp.
T
(
x
+
y
)
-
T
(
x
)
-
T
(
y
)
∈
Z
and
T
(
x
y
)
-
T
(
x
)
T
(
y
)
∈
Z
). We discuss existence of such maps which are not derivations or endomorphisms, we study their effect on
Z
, and we give some commutativity results. |
|---|---|
| ISSN: | 0138-4821 2191-0383 |
| DOI: | 10.1007/s13366-015-0244-8 |