| Popis: |
Right ideals and right submodules need not coincide in an arbitrary nearring. Let T0(G) be the near-ring of all transformations of a group (G, +) int itself that map 0 into 0. Theorem 1. If G is a finite group which contains mor than two elements, then right ideals and normal right submodules of T0(G) coincide if and only if G is noncommutative. Theorem 2. If G is an infinit group, then right ideals and normal right submodules of T0(G) coincide if an only if there exists x ϵ G such that the cardinality of the set of left cosets of the centralizer of x is equal to the cardinality of G. |
