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Some properties of skew-symmetric elements of a ring

Published online by Cambridge University Press:  24 October 2008

I. A. Barnett  and
S. Abian
I. A. Barnett
Affiliation:
University of Cincinnati
S. Abian
Affiliation:
University of Tennessee
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Extract

Let R* be a ring with unit element I. For every A ∈ R*, let the mapping A → A′ be an involutory anti-automorphism, i.e. a one-to-one mapping of R* onto itself with the following properties:

Let C* denote the set of all symmetric elements of R*, i.e. C′ = C for all C ∈ C*.

An element A ∈ R* is said to be skew-symmetric if A′ + A = 0 (the zero element of the ring).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 3 , July 1957 , pp. 549 - 553
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCE

(1)Barnett, I. A. and Mendel, C. W.Amer. Math. Mon. 49 (1942), 169.CrossRefGoogle Scholar