On the classification of some classes of Hamiltonian rings (Q682133)

An H-ring is a ring in which all subrings are ideals. The authors study certain subclasses of H-rings. The problem of classification of H-rings has been reduced in the literature to the classification of so-called nil-H-\(p\)-rings for prime integers \(p\), but this latter problem is still open. The authors say that the most important subclass of the class of all nil-H-rings is the class of almost null rings, which are those rings \(R\) which satisfy, for all \(a,b \in R\), (i) \(a^3 = 0\), (ii) \(Ma^2 = 0\) for some square-free integer \(M\) which depends on \(a\), and (iii) \(ab = ka^2 = lb^2\) for some integers \(k,l\). In this paper the authors classify, up to isomorphism, torsion almost null rings of bounded exponent.