Jordan Ideals and Derivations Satisfying Algebraic Identities
Let N be a 3-prime near-ring with center Z ( N ) and J a nonzero Jordan ideal of N . The aim of this paper is to prove some theorems showing that N must be commutative if it admits a left multiplier F satisfying any one of the following properties: ( i ) F ( J ) ⊆ Z ( N ) , ( i i ) F ( J 2 ) ⊆ Z ( N...
Saved in:
| Published in | Bulletin of the Iranian Mathematical Society Vol. 44; no. 6; pp. 1543 - 1554 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Springer Singapore
01.12.2018
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Summary: | Let
N
be a 3-prime near-ring with center
Z
(
N
)
and
J
a nonzero Jordan ideal of
N
. The aim of this paper is to prove some theorems showing that
N
must be commutative if it admits a left multiplier
F
satisfying any one of the following properties:
(
i
)
F
(
J
)
⊆
Z
(
N
)
,
(
i
i
)
F
(
J
2
)
⊆
Z
(
N
)
,
(
i
i
i
)
F
(
i
j
)
+
[
i
,
j
]
∈
Z
(
N
)
,
(
v
i
)
F
(
i
j
)
-
i
j
+
j
i
∈
Z
(
N
)
,
(
v
)
F
(
i
∘
j
)
∈
Z
(
N
)
and
(
v
i
)
F
(
i
)
G
(
j
)
∈
Z
(
N
)
,
for all
i
,
j
∈
J
.
Moreover, we give some examples which show that the hypotheses placed in our results are not superfluous. |
|---|---|
| ISSN: | 1017-060X 1735-8515 |
| DOI: | 10.1007/s41980-018-0106-x |