Geodesic
States on basic algebras
Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 197-210 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 are the certain pastings of Boolean algebras the construction of a state-morphism is shown.
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 are the certain pastings of Boolean algebras the construction of a state-morphism is shown.
DOI : 10.21136/MB.2016.0056-14
Classification : 03G25, 06C15, 06D35
Keywords: basic algebra; commutative basic algebra; symmetric basic algebra; state; homomorphism 
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Chajda, Ivan; Länger, Helmut. States on basic algebras. Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 197-210. doi: 10.21136/MB.2016.0056-14

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