Soft Computing

, Volume 21, Issue 10, pp 2469–2476

Generalized Łukasiewicz rings

Focus

Abstract

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.

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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Copyright information

© 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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