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Example of a Ring with an Improper Involution
This Demonstration shows an example of an improper involution
, that is,
does not imply
. Let
be a commutative ring different from
. If
is the ring of all 2×2 matrices over
, then the involution
is improper. Specifically, for
, if
, then
, even if
.
Contributed by:
Izidor Hafner
SNAPSHOTS
DETAILS
A *-ring (or involutive ring, or ring with involution) is a ring with an involution
:
,
,
.
The example based on matrix inversion is taken from [1, p. 11]. For definitions, see [1, p. 3, p. 10].
Reference
[1] S. K. Berberian,
Baer *-Rings
, New York: Springer-Verlag, 1972.
RELATED LINKS
Involution
(
Wolfram
MathWorld
)
Ring
(
Wolfram
MathWorld
)
Special Regular Rings with Involution
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Example of a Ring with an Improper Involution
"
http://demonstrations.wolfram.com/ExampleOfARingWithAnImproperInvolution/
Wolfram Demonstrations Project
Published: March 9, 2018
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