A NON-COMMUTATIVE GENERALIZATION OF MTL-RINGS | ||
| Journal of Algebraic Systems | ||
| دوره 13، شماره 3، بهمن 2025، صفحه 123-136 اصل مقاله (149.32 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2024.12946.1707 | ||
| نویسندگان | ||
| Samuel Mouchili؛ Surdive Atamewoue* ؛ Selestin Ndjeya | ||
| Department of Mathematics of H.T.T.C., University of Yaounde I, P.O. Box 47, Yaounde, Cameroon. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Pseudo t-norm؛ Pseudo MTL-Algebra؛ non-commutative ring؛ non-noetherian ring؛ valuation ring | ||
| مراجع | ||
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