February 1, 2018 at 6:30 pm

Ring Theory Seminar | Infinite Dimensional Algebras with no Simple Bases, Feb. 23

The Ohio University Ohio State University Ring Theory Seminar presents Dr. Pinar Aydogdu (Hacettepe University, Ankara, Turkey) discussing “Infinite Dimensional Algebras with no Simple Bases” on Friday, Feb. 23, from 4:45-5:45 p.m. in Cockins Hall 240, OSU-Columbus.

Dr. Pınar Aydoğdu, portrait

Dr. Pınar Aydoğdu

Abstract: Following \cite{ALM}, a basis $B$ over an infinite dimensional $F$-algebra $A$ is amenable if for all $r\in A$, the set of the coordinate vectors of the family $\{rb|b\in B\}$ with respect to $B$ is summable. A basis $B$ is said to be congenial to a basis $C$ if the coordinate vectors of the elements of $B$ represented with respect to $C$ is summable. If $B$ is congenial to $C$ but $C$ is not congenial to $B$, then we say that $B$ is properly congenial to $C$. An amenable basis $B$ is called simple if it is not properly congenial to any other amenable basis. In \cite{ALM}, the fundamental question whether all algebras have simple bases has been raised. In this work, using a construction inspired by that in \cite{KS} and \cite{OW}, we introduce a family of algebras granting us examples of algebras without simple bases and of one-sided simple bases.

This is a joint work with Sergio R. Lopez-Permouth, Professor of Mathematics at Ohio University, and graduate student Rebin A. Muhammad.

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