Geodesic
States on basic algebras
Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 197-210

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MR Zbl
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 
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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[1] Botur, M., Halaš, R., Kühr, J.: States on commutative basic algebras. Fuzzy Sets Syst. 187 (2012), 77-91. | DOI | MR | JFM

[2] Chajda, I.: Basic algebras and their applications. An overview. Proc. 81st Workshop on General Algebra (J. Czermak et al., eds.) Salzburg, Austria, 2011, Johannes Heyn, Klagenfurt (2012), 1-10. | MR | JFM

[3] Chajda, I., Halaš, R.: On varieties of basic algebras. Soft Comput. 19 (2015), 261-267. | DOI | JFM

[4] Kalmbach, G.: Orthomodular Lattices. London Mathematical Society Monographs 18. Academic Press, London (1983). | MR | JFM

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