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Abstract
The recent development of the theory of functional identities is based on the concept of d-freeness introduced by Beidar and Chebotar. This concept involves two conditions, the first one concerns the situation when the expression ∑ i E i x i + ∑ j x j F j is always zero, and the second one the situation when this expression is always central. We discuss the relationship between these two conditions and in particular we establish that in general they are independent of each other.
Acknowledgments
The author is indebted to Martindale W. S. for fruitful discussions from which the questions considered in this article arose. Thanks are also due to the referee for careful reading of the article. The author was supported by a grant from the Ministry of Education, Science and Sport of Slovenia.