[Todos CMAT] SEMINARIO DE ALGEBRA Y TEMAS AFINES EL PROXIMO LUNES

[Walter Ferrer]

​*Falto el nombre del conferencista que va adjunto ahora​*

Seminario de álgebra y temas afines
> Centro de Matemática: Sala de seminarios del piso 14
> Hora: 1430/16 --luego haremos un modesto brindis--
> Día: Lunes 13 de julio de 2015
> Título: "Euclidean pairs, decomposition into idempotents and related
> topics"
>
​   Expositor: André Leroy--Univ. d'Artois, Francia. ​


>
> Resumen :
>
> An ordered pair (a,b) in any ring R is said to be a
> right Euclidean pair if there exist elements (q_{1},r_{1}), ....,
>
> (q_{n+1},r_{n+1}) en R^{2} (for some n\geq 0)
>
> such that a=bq_{1}+r_{1}, b=r_{1}q_{2}+r_{2}, and
>
> r_{i-1}=r_iq_{i+1}+r_{i+1} for 1<i\leq n, r_{n+1}=0.
>
>
>
> If  all pairs (a,b)\in R^2 are
>
> right Euclidean, we say that R is a right quasi-Euclidean
>
> ring.  A nice class of quasi euclidean rings is the class of unit
>
> regular rings.
>
>
> We study the interplay between the classes of right quasi-Euclidean
>
> rings and right K-Hermite rings, and relate them to projective-free
>
> rings and Cohn's GE_2-rings using the method of noncommutative
>
> Euclidean divisions and matrix factorizations into idempotents.
>
> Right quasi-Euclidean rings are closed under matrix extensions, and
>
> a left quasi-Euclidean ring is right quasi-Euclidean if and only if
>
> it is right B\'ezout.   Singular matrices over left and right
>
> quasi-Euclidean domains are shown to be products of idempotent
>
> matrices, generalizing an earlier result of Laffey for singular
>
> matrices over commutative Euclidean domains.
>
>
> Noncommutative continuant polynomials will naturally appear in
>
> connection with quasi euclidean pairs, and, if time permits, we
>
> will also give some of their properties.
>
> We will try to mention also some more recent works related to
>
> decomposition of nonneg
> ​a​
> tive matrices.
>
>
>
> ​
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