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SUMMARY:The universal *-regularization of a ring
DTSTART:20240509T123000Z
DTEND:20240509T133000Z
DTSTAMP:20240530T163900Z
UID:indico-event-279@events.dm.unipi.it
DESCRIPTION:Speakers: Sonia L'Innocente (Università di Camerino)\n\nOlivi
er's construction of the universal commutative (von Neumann) regular ring
over a commutative ring is generalized to obtain the universal $*$-regular
ring over a noncommutative ring $(R\, *)$ with involution. The constructi
on of a universal $*$-regular ring proceeds similarly with the Moore–Pen
rose inverse replacing the role of the group inverse in the construction o
f universal abelian regular rings.Under an algebraic point of view\, some
nice properties of these rings will be described and some nice examples wi
ll be given in this context\, such as the Jacobson algebra.Under the mod
el theoretical point of view\, we can observe thatthe involution of $(R\,
*)$ induces an involution on the modular lattice $L(R\, 1)$ of positive pr
imitive formulae in the language of left $R$-modules. It is shown that $*$
-regular ring coordinatizes the quotient lattice of $L(R\, 1)$ modulo the
least congruence for which the involution designates an orthogonal complem
ent.\n\nhttps://events.dm.unipi.it/event/279/
LOCATION:Aula Riunioni (Dipartimento di Matematica)
URL:https://events.dm.unipi.it/event/279/
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