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Radically principal MV-algebras

  • Olivier A. Heubo-Kwegna and Jean B. Nganou EMAIL logo
Published/Copyright: February 15, 2023
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Abstract

An MV-algebra A is radically principal if every prime ideal P of A is radically principal, i.e., there exists a principal ideal I of A such that Rad ( P ) = Rad ( I ) . We investigate radically principal MV-algebras and provide some characterizations as well as some classes of examples. We prove a Cohen-like theorem, precisely, an MV-algebra is radically principal if and only if every maximal ideal is radically principal. It is also shown that the radically principal hyperarchemedian MV-algebras are the weakly finite ones and the radically principal Boolean algebras are the finite ones. Radically principal MV-algebras are also studied from the perspective of lattice-ordered groups.


This research was partially supported for the first author by the SVSU Braun Fellowship and for the second author by the UHD’s ORCA grant. In addition, the authors are grateful to the referee for his/her comments that improve the quality of the paper.


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Received: 2021-10-05
Accepted: 2022-01-30
Published Online: 2023-02-15
Published in Print: 2023-02-23

© 2023 Mathematical Institute Slovak Academy of Sciences

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