Regularity of generalized MV-algebras

• Autorzy: Chajda, I. , Dorfer, G. , Halaš, R.
• Języki publikacji: EN

Abstrakty

EN

A generalized MV algebra is constructed by means of an 1-group m a way similar to that an MV-algebra is related to a commutative 1-group, see e.g. [11], [9]. We prove that the variety of generalized MV-algebras is congruence regular and give an explicit description of congruence classes.

Słowa kluczowe

EN

congruence regularity; l-group; MV-algebra

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 1
• Strony: 25-32
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Chajda, I.

• Department of Algebra and Geometry Faculty of Sciences Palacky University Olomouc Tomkova 40 Cz 779 00 Olomouc, Czech Republic,

autor

Dorfer, G.

• Institute of Algebra and Computational Mathematics Vienna University of Technology Wiedner Hauptstr. 8-10/118 A-1040 Vienna, Austria,
• Institute of Discrete Mathematics Austrian Academy of Sciences Sonnenfelsgasse 19/2 A-1010 Vienna, Austria

autor

Halaš, R.

• Department of Algebra and Geometry Faculty of Sciences Palacky University Olomouc Tomkova 40, CZ 779 00 Olomouc, Czech Republic,

Bibliografia

• [1] R. Bělohlávek , MV-algebras don't have a single regularity term, preprint.
• [2] I. Chajda , Locally regular varieties, Acta Sci. Math. (Szeged) 64 (1998), 431-435.
• [3] I. Chajda , R. Halaš , J. Rachůnek , Ideals and congruences in generalized MV-algebras, Demonstratio Math. 33 (2000), 213-222.
• [4] C. C. Chang , Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
• [5] C. C. Chang , A new proof of the completeness of the Lukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74-80.
• [6] B. Csakany , Characterization of regular varieties, Acta Sci. Math. (Szeged) 31 (1970), 187-189.
• [7] A. DiNola , A. Lettieri , Equational characterization of all varieties of MV-algebras, J. Algebra 221 (1999), 463-474.
• [8] A. Dvurecenskij , B. Riecan , Weakly divisible MV-algebras and product, J. Math. Anal. Appl. 234 (1999), 208-222.
• [9] A. Dvurecenskij , Pseudo MV-algebras are intervals in l-groups, (2000), submitted.
• [10] G. Georgescu , A. Iorgulescu , Pseudo MV-algebras, to appear in Mult.-Valued Logic.
• [11] D. Mundici , Interpretation of AF C*-algebras in Lukasiewicz sentenial calculus, J . Funct. Anal. 65 (1986), 15-63.
• [12] J. Rachůnek , A non-commutative generalization of MV-algebras, Czechoslovak Math. J., to appear.