Delfino Nolasco
Ohio University
Title
M_{n}(F[x]) is neither Right nor Left duo for any $n >= 2$
Abstract
The main purpose of this presentation is to show that $M_n(F[x])$ is neither Left nor Right Duo where $F$ is an arbitrary field and $n\ge 2$. We are also able to extend our results to $M_n(R)$ for any $n\ge 2$, where $R$ is an infinite dimensional $F$-Algebra, and $F$ is a field . In order to show this, we need to understand the concept of $B$ being Right Amenable and Left Amenable Basis for $R$. We explore the properties of $B$ Right Amenable and Left Amenable Basis of $R$. We are able to extend our definition to $B$ is right amenably congenial (Left) Amenable to $C$. This new definition helps to guarantee when $M_n(R)$ is Right or Left Amenable. We present many examples using $F[x]$ and $M_2(F[x])$. Finally we
consider $R$ an Algebra with Involution. We show that a lot of the results for $M_n(F[x])$ are also true when $R$ is an Algebra with Involution.
Zoom Link: https://osu.zoom.us/j/98492698311?pwd=yimtIdmH6TKoCbW9h7kQssTJSLEU5V.1