Abstract:
In this paper a number of theorems are obtained on decompositions of Artinian alternative rings, generalizing analogous theorems of Szász, Shneidmyuller, Kertész et al. for associative Artinian rings. For example, it is shown that every alternative Artinian ring decomposes into a direct sum of torsion parts and a torsion free ideal. With several additional restrictions, we obtain a decomposition of any alternative Artinian ring into a direct sum of an ideal and a left ideal, allowing a rather detailed description. A description of hereditarily Artinian alternative rings is given.
Bibliography: 16 titles.