Complementation in the Group of Units of Matrix Rings

Details Complementation in the Group of Units of Matrix Rings Complementation in the Group of Units of Matrix Rings

2010-10-07

arxiv.org/abs/1010.1332v1

Bulletin of the Australian Mathematical Society 70, no. 2, pp223-227, 2004

Mathematics

Group Theory

Scientific paper

Let $R$ be a ring with $1$ and $\J(R)$ its Jacobson radical. Then $1+\J(R)$
is a normal subgroup of the group of units, $G(R)$. The existence of a
complement to this subgroup was explored in a paper by Coleman and Easdown; in
particular the ring $R=\Mat_n(\Z_{p^k})$ was considered. We prove the remaining
cases to determine for which $n$, $p$ and $k$ a complement exists in this ring.

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