BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Irene Paniello (University of Zaragoza\, Spain) DTSTART:20250901T150000Z DTEND:20250901T160000Z DTSTAMP:20260423T035715Z UID:ENAAS/135 DESCRIPTION:Title: Local inheritance in Jordan algebras of quotients\nby Irene Paniello ( University of Zaragoza\, Spain) as part of European Non-Associative Algebr a Seminar\n\n\nAbstract\nSince their introduction by K. Meyberg in the non associative setting\, local algebras have played a key role in the study o f Jordan systems. The local inheritance of regularity conditions (such as nondegenerancy\, strong primeness or primitivity) is a well-known result that undoubtedly contributed to the development of the structure theory \, not only of Jordan algebras\, but also of Jordan pairs and triple syste ms. \n\nA rather usual strategy to tackle many Jordan questions is to d ifferentiate Jordan systems depending on whether their\n local algebras satisfy or not certain properties. For instance\, some of the recent r esults on localization theory for Jordan algebras have been established t aking advantage of the \n dichotomy between Jordan algebras having\, or not\, local algebras satisfying polynomial identities.\nAnalogously\, the formulation of Goldie local theory for Jordan algebras is closely re lated to Jordan algebras \nadmitting Lesieur-Croisot local algebras.\n \ n \n The above considerations lead us to consider\, in the Jordan algebra setting\, how local algebras of Jordan algebras interact with their algeb ras of quotients (in Utumi's sense). This problem is motivated by a prev ious question originally posed\, in the associative setting for (maximal \, Martindale and symmetric) rings of quotients of semiprime rings by G\\' omez Lozano and Siles Molina\, who proved that both constructions commute whenever the element at which the local algebra is defined becomes von Neu mann regular in the corresponding ring of quotients. \n \n In this talk we will display the Jordan algebra case of this problem\, proving that\, for any nondegenerate Jordan algebra\, whenever the element defining the local algebra becomes von Neumann regular in its maximal algebra of quot ients\, taking local algebras and maximal algebras of quotients are comm uting constructions.\n \n \nThis is a joint work with Fernando Montaner (U niversity of Zaragoza).\n LOCATION:https://researchseminars.org/talk/ENAAS/135/ END:VEVENT END:VCALENDAR