Abstract
UDC 512.5
Let
ℛ
be a unital
*
-ring with the unit
I
. Assume that
ℛ
contains a symmetric idempotent
P
which satisfies
A
ℛ
P
=
0
implies
A
=
0
and
A
ℛ
(
I
-
P
)
=
0
implies
A
=
0
. In this paper, it is proved that if
ϕ
:
ℛ
→
ℛ
is a nonlinear skew commuting map, then there exists an element
Z
∈
𝒵
S
(
ℛ
)
such that
ϕ
(
X
)
=
Z
X
for all
X
∈
ℛ
, where
𝒵
S
(
ℛ
)
is the symmetric center of
ℛ
.As an application, the form of nonlinear skew commuting maps on factors is obtained.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science