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On varieties of MV-algebras with internal states |
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| Authors: | A Di Nola A Lettieri |
| Institution: | a Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte don Melillo, I-84084 Fisciano, Salerno, Italy b Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia c Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli Federico II, via Monteoliveto 3, I-80134 Napoli, Italy |
| Abstract: | In 4] and 5] the authors introduced the variety SMV of MV-algebras with an internal operator, state MV-algebras. In 2] and 3] the authors gave a stronger version of state MV-algebras, called state-morphism MV-algebras. In this paper we continue the studies presented in 2] and 3] just looking at several proper subvarieties of SMV, obtained by imposing suitable conditions on the behavior of the internal operator. |
| Keywords: | State MV-algebra Internal state State-morphism MV-algebra State-morphism-operator Subdirectly irreducible state MV-algebra |
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