Generalized Łukasiewicz rings
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This paper extends the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola (Math Log Q 55(5):468–486, 2009) 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 up to isomorphism, these are exactly the direct sums of unitary special primary rings.
KeywordsMV-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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Conflict of interest
The authors declare that they have no conflict of interest.
- Chajda I, Khür J (2006) GMV-algebras and meet-semilattices with sectionally antitone permutations. Math Slovaca 56:275–288Google Scholar
- Cignoli R, D’Ottaviano I, Mundici D (2000) Algebraic foundations of many-valued reasoning. Kluwer, DordrechtGoogle Scholar
- Georgescu G, Iorgulescu A (1999) Pseudo-MV algebras: a non-commutative extension of MV algebras. In: Proc 4th International Symposium of Economics Informatics. IN-FOREC Printing House, Bucharest, pp 961–968Google Scholar
- Wadsworth AR (1987) Dubrovin valuation rings. In: Van Oystaeyen F, Le Bruyn L (eds) Perspectives in ring theory. Springer, Netherlands, pp 359–374Google Scholar