## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, January 14, 2016 — 11:30 AM EST

**Ehsaan Hossain, Pure Mathematics, University of Waterloo**

"Morita theory 1: Modules"

Let $\mathrm{Mod}_R$ be the category of right $R$-modules. Two rings $R,S$ are \textit{Morita equivalent}, denoted $R\sim S$, if $\mathrm{Mod}_R$ and $\mathrm{Mod}_S$ are equivalent as categories. For example $\mathbf{C}$ is Morita equivalent to $M_2(\mathbf{C})$, because any $\mathbf{C}$-vector space can double up to become an $M_2(\mathbf{C})$-module. Many properties are Morita invariant; for instance simplicity, semisimplicity, and chain conditions.

In the first half of this semester, we aim to cover Morita's fundamental theorems, which give surprisingly down-to-earth characterizations of when two rings are Morita equivalent. We'll need some basic module theory, namely projective and injective modules. We'll also need that when we do more localization later, so it'll pay off.

Location

MC 5403

,

Canada

,

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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