A NON-COMMUTATIVE GENERALIZATION OF MTL-RINGS
نویسندگان
1 Department of Mathematics of H.T.T.C., University of Yaounde I, P.O. Box 47, Yaounde, Cameroon.
2 Department of Mathematics of H.T.T.C., University of Yaounde I, P.O. Box 47, Yaounde, Cameroon.
3 Department of Mathematics of H.T.T.C., University of Yaounde I, P.O. Box 47, Yaounde, Cameroon.
doi
10.22044/jas.2024.12946.1707چکیده
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.
