Two notions of MV-algebraic semisimplicity relative to fixed MV-chains

Abstract

We initiate a study of two general concepts of semisimplicity for MV-algebras by replacing the standard MV-algebra $[0,1]$ with an arbitrary MV-chain $\mathbf{C}$. These generalised notions are called $\mathbf{C}$-semisimple MV-algebras and $\mathfrak{m}$-semisimple MV-algebras. We obtain several of their characterisations and explore in more-depth the case of perfect MV-chains.

Keywords:

• MV-algebra
• $\mathbf{C}$-semisimple
• maximal ideal
• $\mathbf{C}$-radical
• Chang's MV-algebra

2010 Mathematics Subject Classifications:

• 06D35
• 06E15
• 06D50

Disclosure statement

No potential conflict of interest was reported by the author(s).

Acknowledgment

The second author is grateful to UHD for the Funded Faculty Leave during which a portion of the paper was completed.