On a non-commutative Generalization of Lukasiewicz rings
  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. 
J.B. Nganou, C. Lele, A. Kadji
math.LO math.RA