## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, January 12, 2017 - 4:00 PM EST

**Hongdi Huang, Pure Mathematics, University of Waterloo**

"On *-clean group algebras"

A ring $R$ is called a $*$-ring (or a ring with involution $*$) if there exists an operation $*$: $R \rightarrow R$ such that $(x+y)^*=x^*+y^*, \,\ (xy)^*=y^*x^* \,\ $ and $(x^*)^*=x$,

for all $x, y\in R$. An element in a ring $R$ is called $*$-clean if it is the sum of a unit and a projection ($*$-invariant idempotent). A $*$-ring is called $*$-clean if each of its elements is the sum of a unit and a projection.

It is interesting to investigate the $*$-cleanness of $F_qG$, where $F_q$ is a finite field and $G$ is a finite cyclic group. Moreover, we will consider when the group algebras of the dihedral groups $D_{2n}$, and the generalized quaternion groups $Q_{2n}$ with standard involution $*$ over a ring $R$ are $*$-clean.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

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