# Equivalence of Projections in Involutive Rings

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Let be a ring with involution , that is, . An element is called a projection if it is self-adjoint () and idempotent (). The projections and are said to be equivalent, written , when exists such that and . Projections are algebraically equivalent if there exist and such that and .

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Contributed by: Izidor Hafner (March 2018)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This example and definitions were taken from [1, pp. 3–10].

References

[1] S. K. Berberian, *Baer *-Rings*, New York: Springer-Verlag 1972.

[2] I. Kaplansky, *Rings of Operators*, New York: W. A. Benjamin, 1968.

## Permanent Citation

"Equivalence of Projections in Involutive Rings"

http://demonstrations.wolfram.com/EquivalenceOfProjectionsInInvolutiveRings/

Wolfram Demonstrations Project

Published: March 12 2018