College of Liberal Arts & Sciences

# Algebra Seminar

Speaker:

Jeremy Edison

Topic:

"Invertible and I2 Bases for Field Extensions"

**Abstract: **

An algebra $A$ over a field $\mathbb{K}$ is said to be invertible if it has a basis $\mathcal{B}$ consisting solely of units. If $\mathcal{B}$ is an invertible basis such that $\mathcal{B}^{-1}$ is again a basis, $A$ is said to be an I2 algebra. It is currently not known whether an algebra which is invertible is necessarily I2.

If $\mathbb{L}/\mathbb{K}$ is any extension of fields, then $\mathbb{L}$ is clearly an invertible $\mathbb{K}$ algebra. In this talk we prove that if $\mathbb{K}$ is infinite, then $\mathbb{L}$ is in fact an I2 algebra.

Event Date:

February 12, 2018 - 3:30pm to 4:30pm

Location:

214 MLH

Calendar Category:

Seminar