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Hyper Commutative Basic Algebras, Hyper MV-algebras, and States
Jing Wang, Yali Wu and Yichuan Yang

In this paper, we introduce hyper commutative basic algebras. We first prove that every hyper MV-algebra is a hyper commutative basic algebra. Then we show that a hyper commutative basic algebra of cardinality 2 is a hyper MV-algebra, which is similar to the result of Botur and Halaš that finite commutative basic algebras coincide with MV-algebras. However, we find a hyper commutative basic algebra of cardinality 3 which is not a hyper MV-algebra. Finally, we study two types of states on hyper commutative basic algebras.

Keywords: Hyper commutative basic algebras, hyper MV-algebras, sup-states, Riĕcan states

MSC(2010): 06D35, 03G25.

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