Displaying similar documents to “Spectral States of Commutative L.m.c. Algebras”

States on basic algebras

Ivan Chajda, Helmut Länger (2017)

Mathematica Bohemica

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States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which...