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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