Soft Computing

, Volume 21, Issue 10, pp 2469–2476 | Cite as

Generalized Łukasiewicz rings



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.


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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Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Yaoundé IYaoundéCameroon
  2. 2.Department of Mathematics and Computer ScienceUniversity of DschangDschangCameroon
  3. 3.Department of MathematicsUniversity of OregonEugeneUSA

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