BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Fernando Montaner (University of Zaragoza\, Spain) DTSTART:20241104T150000Z DTEND:20241104T160000Z DTSTAMP:20260423T021313Z UID:ENAAS/102 DESCRIPTION:Title: Pairs of quotients of Jordan pairs\nby Fernando Montaner (University o f Zaragoza\, Spain) as part of European Non-Associative Algebra Seminar\n\ n\nAbstract\nIn this talk we expose ongoing joint work with I Paniello on systems of quotients (in a sense partially extending the localization theo ry of Jordan algebras\, which in turn is inspired by the localization theo ry of associative algebras). Localization theory in associative algebras o riginated in the purpose of extending the construction of fields of quotie nts of integral domains\, and therefore in the purpose of defining ring e xtensions in which a selected set of elements become invertible. As it is well known in associative theory that led to Goldie's theorems\, and thes e in turn to more general localization theories for which the denominators of the fraction-like elements of the extensions are (one-sided) ideals ta ken in a class of filters (Gabriel filters). These ideas have been partial ly extended to Jordan algebras by several authors (starting with Zelmanov' s version of Goldie theory in the Jordan setting\, and its extension by Fe rnandez López-García Rus and Montaner) and Paniello and Montaner (among others) definition of algebras of quotients of Jordan algebras. Following the development of Jordan theory\, a natural direction for extending these results is considering the context of Jordan pairs. This is the objective of the research presented here. Since obviously a Jordan pair cannot have invertible elements unless it is an algebra\, and in this case we are bac k in the already developed theory\, the kind of quotients that would make a significative (proper) extension of the case of algebras should be based in a different notion of quotient. An approach that seems to be promisin g is considering the Jordan extension of Fountain and Gould notion of loca l order\, as has been adapted to Jordan algebras by the work of Fernández López\, and more recently by Montaner and Paniello with the notion of lo cal order\, in which the bridge between algebras and pairs is established by local algebras following the ideas of D'Amour and McCrimmon. In the tal k this idea is exposed\, together with the state of the research\, and the open problems that it raises.\n LOCATION:https://researchseminars.org/talk/ENAAS/102/ END:VEVENT END:VCALENDAR