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A non-commutative generalization of Łukasiewicz rings |
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| Institution: | 1. Department of Mathematics, University of Yaounde I, Cameroon;2. Department of Mathematics and Computer Science, University of Dschang, Cameroon;3. Department of Mathematics, University of Oregon, Eugene, OR 97403, United States |
| Abstract: | 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 1] to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Łukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings. |
| Keywords: | MV-algebra Łukasiewicz ring QF-ring Pseudo MV-algebra Semi-ring Special primary ring Dubrovin valuation ring Brown–McCoy radical Jacobson radical |
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