Jacobson radical of Artinian (2,n)-rings (Q1057972)

By analogy with ordinary rings the notion of the Jacobson radical for (2,n)-rings is introduced (these are additive commutative groups with an n-ary operation of multiplication, which is associative and distributive relative to the addition). A complete description of the Jacobson radical for artinian (2,n)-rings is obtained. Namely, the equality \(J(R)=J(S(R))\cap R\) is proved, where R is an artinian (2,n)-ring and S(R) is its standard covering ring.