Geodesic
A characterization of commutative basic algebras
Mathematica Bohemica, Tome 134 (2009) no. 2, pp. 113-120

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MR Zbl
A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
DOI : 10.21136/MB.2009.140646
Classification : 03G10, 06D35, 06F35
Keywords: lattice with section antitone involution; basic algebra; commutative basic algebra; MV-algebra 
Chajda, Ivan. A characterization of commutative basic algebras. Mathematica Bohemica, Tome 134 (2009) no. 2, pp. 113-120. doi: 10.21136/MB.2009.140646
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[1] Botur, M., Halaš, R.: Finite commutative basic algebras are MV-algebras. (to appear) in Multiple-Valued Logic and Soft Computing.

[2] Chajda, I.: Lattices and semilattices having an antitone involution in every upper interval. Comment. Math. Univ. Carol. 44 (2003), 577-585. | MR | Zbl

[3] Chajda, I., Emanovský, P.: Bounded lattices with antitone involutions and properties of MV-algebras. Discuss. Math., Gener. Algebra Appl. 24 (2004), 31-42. | DOI | MR | Zbl

[4] Chajda, I., Halaš, R.: A basic algebra is an MV-algebra if and only if it is a BCC-algebra. Int. J. Theor. Phys. 47 (2008), 261-267. | DOI | MR | Zbl

[5] Chajda, I., Halaš, R., Kühr, J.: Distributive lattices with sectionally antitone involutions. Acta Sci. Math. (Szeged) 71 (2005), 19-33. | MR | Zbl

[6] Cignoli, R. L. O., D'Ottaviano, M. L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning. Kluwer Acad. Publ., Dordrecht (2000). | MR | Zbl

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