## 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

**Returning to in-person experiences in February:** Visit the COVID-19 website for more information.

Tuesday, November 24, 2015 — 11:30 AM EST

**Christopher Schafhauser, Department of Pure Mathematics, University of Waterloo **

“Goldie’s Theorem on semiprime rings”

Recall that R is a right Ore ring if its set S = C(R) of cancelable elements satisfies the right Ore condition. In this case we can form the right classical ring of fractions Q = RS−1, and there is a natural inclusion R Q such that S ⊆ Q× and each element of Q has the form as−1,forsomea∈Rands∈S. WesawthatifRisadomainthenQisadivisionring,but this fails if R is not right Ore — in fact, in the non-Ore case we can’t form the right ring of fractions. But we can still ask whether or not R embeds in some ring Q such that S ⊆ Q× and each element of Q has the form as−1. In this case R is called a right order in Q.

Our aim now is to determine when R is a right order in a semisimple ring. For this, there are necessary and sufficient conditions given by Goldie’s Theorem.

MC 5403

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

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.