Structure of Clifford Semigroups of Matrices

Details Structure of Clifford Semigroups of Matrices Structure of Clifford Semigroups of Matrices

2010-06-22

arxiv.org/abs/1006.4301v1

Mathematics

Group Theory

9 pages

Scientific paper

In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a subdirect product of some linear (0-)groups. Then we generalize this result to a semigroup of matrices of countably infinite order and give a similar necessary and sufficient condition for it to be a Clifford semigroup.

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