Compact nonassociative rings (Q793139)

An infinite simple compact (not necessarily associative) ring is 0- dimensional, of countable local weight and its cardinality is equal to the continuum (theorem 1). Each 0-dimensional compact ring from a variety satisfying conditions due to Zhevlakov-Shestakov has a local base consisting of open ideals (theorem 2) and is finite, if it is simple (theorem 3). If a compact ring A belongs to such a variety all of whose finite nil rings are nilpotent, then every nil subring of A is pronilpotent (theorem 5).