  The goal of the present article is to extend the study of commutative rings
whose ideals form an MV-algebra as carried out by Belluce and Di Nola to
non-commutative rings. We study and characterize all rings whose ideals form a
pseudo MV-algebra, which shall be called here generalized Lukasiewicz rings. We
obtain that these are (up to isomorphism) exactly the direct sums of unitary
special primary rings.
