Corrigendum to inner Rickart and Baer Jordan algebras
Farhodjon ArzikulovAndijan State University, Andijan, UzbekistanU. I. KhakimovAndijan State University, Andijan, Uzbekistan
ABI
Abstract
In the present paper corrected versions of the statements in the paper "Description of finite-dimensional inner Rickart and Baer Jordan algebras" by F.N. Arzikulov and U.I. Khakimov are given. In particular, it is shown that for any Jordan algebra J with an idempotent p and an associative degenerate radical D such that J=Fp+̇D, J is an inner RJ-algebra if and only if, for any nonzero a∈D, a2=0 and p(pa) = pa. Also, other equivalent conditions when a Jordan algebra J is an inner RJ-algebra are given. As for finite-dimensional nilpotent Jordan algebras, there is not a nilpotent inner RJ-algebra (and hence inner BJ-algebra) except the finite-dimensional Jordan algebra the square of each element of which is zero.
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