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
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.
Comments