State-morphism MV-algebras

doi:10.1016/j.apal.2009.05.003

Annals of Pure and Applied Logic

Volume 161, Issue 2, November 2009, Pages 161-173

Dedicated to Franco Montagna on the occasion of his 60th birthday.

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Abstract

We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such (state-morphism) state MV-algebras with the category of unital Abelian $ℓ$ -groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras.

MSC

06D35

03G12

03B50

Keywords

MV-algebra

State

Extremal state

State-morphism

State MV-algebra

State-morphism MV-algebra