Nonassociative topological bimodules

The local structure of locally compact bimodules over compact rings is studied. It is shown that topologically simple compact alternative, Jordan, and restricted Lie rings are finite. An example of a simple compact nondiscrete Lie ring is given. The quasiregular radical of an alternative or Jordan compact ring is characterized as the intersection of the kernels of all its locally compact topologically irreducible birepresentations.
Bibliography: 17 titles.