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On skew-commuting mappings of rings

Published online by Cambridge University Press:  17 April 2009

Matej Brešar
Matej Brešar
Affiliation:
University of Maribor PF, Koroška 160 62000 Maribor, Slovenia
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Abstract

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A mapping f of a ring R into itself is called skew-commuting on a subset S of R if f(s)s + sf(s) = 0 for all s ∈ S. We prove two theorems which show that under rather mild assumptions a nonzero additive mapping cannot have this property. The first theorem asserts that if R is a prime ring of characteristic not 2, and f: R → R is an additive mapping which is skew-commuting on an ideal I of R, then f(I) = 0. The second theorem states that zero is the only additive mapping which is skew-commuting on a 2-torsion free semiprime ring.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 2 , April 1993 , pp. 291 - 296
Copyright
Copyright © Australian Mathematical Society 1993

References

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