On the geometry of associativity

Semigroup Forum

Volumn 74, Issue 3, 2007, Pages 439-466

  Jenei, Sandor ^a  

^a UNIVERSITY OF PÉCS   (Hungary)

Author keywords

Associativity; Residuated lattice; Rotation invariance

Indexed keywords

EID: 34547602951     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00233-006-0673-7     Document Type: Article

References (27)

1. Abel, N. H., Untersuchungen der Functionen zweier unabhängig veränderlichen Grössen x und y wie f(x, y), welche die Eigenschaft haben, dass f(z, f(x, y)) eine symmetrische Function von x, y und z ist, J. Reine Angew. Math. l (1826), 11-15. Oeuvres Complètes de N. H. Abel, Vol. 1, Christiana, 1881, 61-65.
2. Aczél, J., "Lectures on Functional Equations and their Applications", Academic Press, New York, London, 1966.
3. Alsina, C., M. J. Frank and B. Schweizer, Problems on Associative Functions, Aequationes Mathematicae 66 (2003), 128-140.
4. Birkhoff, G., "Lattice Theory", Amer. Math. Soc. Colloquium Publications, third edition, Amer. Math. Soc., Providence, RI, 1973.
5. Blyth, T. S., and M. F. Janowitz, "Residuation Theory", Pergamon Press, 1972.
6. Chang, C. C., Algebraic analysis of many valued logics, TAMS 88 (1958), 467-490.
7. Cignoli, R., I. M. L. D'Ottaviano and D. Mundici, "Algebraic Foundations of Many-Valued Reasoning", Kluwer, Dordrecht, 2000.
8. Clifford, A. H., Naturally totally ordered commutative semigroups, Amer. J. Math. 76 (1954), 631-646.
9. Climescu, A. C., Sur l'équation fonctionnelle de l'associativité, Bull. École Polytechn. Iassy 1 (1946), 1-16.
10. Esteva, F., J. Gispert, L. Godo and F. Montagna, On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic, Studia Logica 71 (2002), 199-226.
11. Esteva, F., and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems 124 (2001), 271-288.
12. Fuchs, L., "Partially Ordered Algebraic Systems", Pergamon Press, Oxford, London, New York, Paris, 1963.
13. Gabbay, D. M., "Semantical Investigations in Heyting's Intuitionistic Logic", D. Reidel, Dordrecht, 1981.
14. Gierz, G. K., K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, "Continuous Lattices and Domains", Encycl. of Math. and its Appl., vol. 93, Cambridge University Press, Cambridge, 2003.
15. Gottwald, S., and S. Jenei, A new axiomatization for Involutive Monoidal T-norm-based Logic, Fuzzy Sets and Systems 124 (2001), 303-308.
16. Hofmann, K. H., and J. D. Lawson, "Linearly Ordered Semigroups: Historical Origins and A. H. Clifford's Influance", in: K. H. Hofmann, M. W. Mislove, eds., "Semigroup Theory and its Applications", Lond. Math. Soc. Lecture Notes, vol. 231, 1996, pp. 15-39.
17. Hofmann, K. H., and P. S. Mostert, "Elements of Compact Semigroups", Ch. E. Merril, Columbus, OH, 1966.
18. Jenei, S., On the convex combination of left-continuous t-norms, Aequationes Mathematicae 72 (2006), 47-59.
19. Jenei, S., On the structure of rotation-invariant semigroups, Archive for Mathematical Logic 42 (2003), 489-514.
20. Johnstone, P. T., "Stone Spaces", Cambridge University Press, Cambridge, 1982.
21. Klement, E. P., R. Mesiar and E. Pap, "Triangular Norms", Kluwer Academic Publishers, Dordrecht, 2000.
22. Lawson, J. D., The earliest semigroup paper?, Semigroup Forum 52 (1996), 55-60.
23. Mostert, P. S., and A. L. Shields, On the structure of semigroups on a compact manifold with boundary, Ann. Math. 65 (1957), 117-143.
24. Noguera, C., F. Esteva and J. Gispert, Perfect and bipartite IMTL-algebras and disconnected rotations of basic semihoops, Archive for Mathematical Logic 44 (2005), 869-886.
25. Rosenthal, K. I., "Quantales and their Applications", Longman Scientific & Technical, Harlow, 1990.
26. Schweizer, B., and A. Sklar, "Probabilistic Metric Spaces", North Holland, New York, 1983.
27. Trillas, E., Sobre funciones de negación en la teoría de conjuntas difusos, Stochastica 3 (1979), 47-60.