| Abstract: | In this note we study the commutative modular and semisimple group rings of  -summable abelian  -groups, which group class was introduced by R. Linton and Ch. Megibben. It is proved that  is  -summable if and only if  is  -summable, provided  is an abelian group and  is a commutative ring with 1 of prime characteristic  , having a trivial nilradical. If  is a  -summable  -group and the group algebras  and  over a field  of characteristic  are  -isomorphic, then  is a  -summable  -group, too. In particular  provided  is totally projective of a countable length. Moreover, when  is a first kind field with respect to  and  is  -torsion,  is  -summable if and only if  is a direct sum of cyclic groups. |
