Shahrood University of Technology Journal of Algebraic Systems 2345-5128 13 3 2025 11 01 A NON-COMMUTATIVE GENERALIZATION OF MTL-RINGS 123 136 3114 10.22044/jas.2024.12946.1707 EN Samuel Mouchili Department of Mathematics of H.T.T.C., University of Yaounde I, P.O. Box 47, Yaounde, Cameroon. Surdive Atamewoue Department of Mathematics of H.T.T.C., University of Yaounde I, P.O. Box 47, Yaounde, Cameroon. 0000-0002-0634-116X Selestin Ndjeya Department of Mathematics of H.T.T.C., University of Yaounde I, P.O. Box 47, Yaounde, Cameroon. Journal Article 2023 04 12 The current work extends the class of commutative MTL-rings established by the authors to the non-commutative ones. That class of rings will be named generalized MTL-rings since they are not necessary commutative. We show that in the non-commutative case, a local ring with identity is a generalized MTL-ring if and only if it is an ideal chain ring. We prove that the ring of matrices over an MTL-ring is a non-commutative MTL-ring. We also study their representation in terms of subdirect irreducibility. https://jas.shahroodut.ac.ir/article_3114_38e5d02e643d3392fadc1c15ec71526c.pdf