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Homogeneous elements of free algebras have free idealizers

Published online by Cambridge University Press:  24 October 2008

Warren Dicks
Warren Dicks
Affiliation:
Bedford College, London
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Abstract

Let k be a field, X a set, F = k 〈X〉 the free associative k-algebra, and b an element of F that is homogeneous with respect to the grading of F induced by some map . We show that the idealizer of b in F, S = {f∈F|fb∈bF}, is a free algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 7 - 26
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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