Complementation in the Group of Units of Matrix Rings

Stewart Wilcox

Complementation in the Group of Units of Matrix Rings

Group Theory 2010-10-08 v1

Authors: Stewart Wilcox

Abstract

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.

Keywords

matrix ring group of units jacobson radical complement normal subgroup

Cite

@article{arxiv.1010.1332,
  title  = {Complementation in the Group of Units of Matrix Rings},
  author = {Stewart Wilcox},
  journal= {arXiv preprint arXiv:1010.1332},
  year   = {2010}
}

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