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Abstract
We study the sets of elements of Jordan pairs whose local Jordan algebras are Lesieur-Croisot algebras, that is, classical orders in nondegenerate Jordan algebras with finite capacity. It is then proved that, if the Jordan pair is nondegenerate, the set of its Lesieur-Croisot elements is an ideal of the Jordan pair.
Acknowledgments
The authors want to thank Professor Fernández López for his kindness in sharing the unpublished results contained in the manuscript Goldie Theory for Jordan pairs authored by A. Fernández López, E. García Rus and F. Montaner.
Additional information
Funding
Fernando Montaner was partially supported by grants MTM2017-83506-C2-1-P (AEI/FEDER, UE) and PID2021-123461NB-C21, funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, and by Diputación General de Aragón (Grupo de Investigación Álgebra y Geometría). Irene Paniello was partially supported by grants MTM2017-83506-C2-1-P (AEI/FEDER, UE) and PID2021-123461NB-C21, funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”.