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GMV-algebras and meet-semilattices with sectionally antitone permutations. (English) Zbl 1141.06002
SAP-semilattices are structures of the form \((S,\wedge ,\circ ,(f_a)_{a\in S})\), where \((S,\wedge , \circ )\) is a meet-semilattice and every \(f_a\) is an antiautomorphism of the order ideal \((a]\). This paper investigates the connections between SAP-semilattices and generalized MV-algebras (= pseudo MV-algebras).

MSC:
06A12 Semilattices
06D35 MV-algebras
03G25 Other algebras related to logic
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References:
[1] CHAJDA I.-EIGENTHALER G.-LANGER H.: Congruence Classes in Universal Algebra. Heldermann Verlag, Lemgo, 2003. · Zbl 1014.08001
[2] CHAJDA I.: Lattices and semilattices having an antitone involution in every upper interval. Comment. Math. Univ. Carolin. 44 (2003), 577-585. · Zbl 1101.06003
[3] CHAJDA I.-HALAŠ R.-KÜHR J.: Distributive lattices with sectionally antitone involutions. Acta Sci. Math. (Szeged) 71 (2005), 19-33. · Zbl 1099.06006
[4] CIGNOLI R. L. O.-D’OTTAVIANO I. M. L.-MUNDICI D.: Algebraic Foundations of Many-Valued Reasoning. Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. · Zbl 0937.06009
[5] DVUREČENSKIJ A.: Pseudo MV-algebras are intervals in t-groups. J. Aust. Math. Soc. 72 (2002), 427-445. · Zbl 1027.06014
[6] DVUREČENSKIJ A.: On pseudo MV-algebras. Soft Comput. 5 (2001), 347-354. · Zbl 1081.06010
[7] GEORGESCU G.-IORGULESCU A.: Pseudo MV-algebras. Mult.-Valued Log. 6 (2001), 95-135. · Zbl 1014.06008
[8] MUNDICI D.: Interpretation of AF C* -algebras in Lukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15-63. · Zbl 0597.46059
[9] RACHŮNEK J.: A non-commutative generalization of MV-algebras. Czechoslovak Math. J. 52 (2002), 255-273. · Zbl 1012.06012
[10] RACHŮNEK J.: Prime spectra of non-commutative generalizations of MV-algebras. Algebra Universalis 48 (2002), 151-169. · Zbl 1058.06015
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