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
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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.
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