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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.

Location
M3 3103

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