**Title:** Some Platitudes on Flatness

**Speaker:** Professor David Benson

**Speaker Info:** University of Georgia

**Brief Description:**

**Special Note**:

**Abstract:**

I shall begin by recalling what it means for a module to be flat, and I shall give an overview of the classical theorems on colimits, projective dimension, cardinality, etc. (As a teaser for this part of the talk, let me mention that if ${\bf C}$ denotes the field of complex numbers then the projective dimension of the flat ${\bf C}[x,y,z]$-module ${\bf C}(x,y,z)$ is equal to two if the continuum hypothesis holds, and three if it fails).In the second half of the talk, I shall concentrate on some recent joint work with Ken Goodearl. The first theorem says that a periodic flat module (over any ring) is necessarily projective. The second theorem is about group rings of finite groups, and says that if $R$ is a coefficient ring and $G$ is a finite group, then a flat $RG$-module which is projective as an $R$-module is also projective as an $RG$-module. There is also a version for infinite groups, which says that cofibrant flat modules are projective.

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