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Abstract
The existence of idempotent elements in plenary train algebras of rank greater than 3, is an open problem to be solved. J. Carlos Gutierrez's results on plenary train algebras in Gutierrez (Citation2000) are based on the underlying assumption of the existence of an idempotent. In this article we study conditions on the scalars defining a plenary train algebra of rank 4 to assure the existence of such an idempotent.
AMS (2000) Subject Classification:
ACKNOWLEDGMENTS
The authors thank the referee for his (or her) valuable suggestions and comments that improve the presentation of the article. Alicia Labra was supported by FONDECYT 1030919. Part of this research was done while this author was visiting Universidad de Chile on a grant from MECESUP-PUC 0103.
Notes
Communicated by I. P. Shestakov.