Previous |  Up |  Next

Article

Keywords:
natural duality; (strong) dualisability; entailment
Summary:
Results saying how to transfer the entailment in certain minimal and maximal ways and how to transfer strong dualisability between two different finite generators of a quasi-variety of algebras are presented. A new proof for a well-known result in the theory of natural dualities which says that strong dualisability of a quasi-variety is independent of the generating algebra is derived.
References:
[1] Clark, D. M., Davey, B. A.: Natural Dualities for the Working Algebraist. Cambridge University Press, Cambridge (1998). MR 1663208 | Zbl 0910.08001
[2] Clark, D. M., Idziak, P. M., Sabourin, L. R., Szabó, Cs., Willard, R.: Natural dualities for quasi-varieties generated by a finite commutative ring. Algebra Universalis 46 (2001), 285-320. DOI 10.1007/PL00000344 | MR 1835800
[3] Davey, B. A., Haviar, M.: A schizophrenic operation which aids the efficient transfer of strong dualitites. Houston Math. J. 26 (2000), 215-222. MR 1814235
[4] Davey, B. A., Haviar, M., Priestley, H. A.: The syntax and semantics of entailment in duality theory. J. Symbolic Logic 60 (1995), 1087-1114. DOI 10.2307/2275875 | MR 1367197 | Zbl 0845.08006
[5] Davey, B. A., Haviar, M., Willard, R.: Structural entailment. Algebra Universalis 54 (2005), 397-416. DOI 10.1007/s00012-005-1944-y | MR 2218853 | Zbl 1090.08009
[6] Davey, B. A., Willard, R.: The dualisability of a quasi-variety is independent of the generating algebra. Algebra Universalis 45 (2001), 103-106. DOI 10.1007/s000120050204 | MR 1809859 | Zbl 1039.08006
[7] Gouveia, M. J., Haviar, M.: Transferral of entailment in duality theory: dualisability. Czech. Math. J. 61 (2011), 41-63. DOI 10.1007/s10587-011-0016-z | MR 2782758
[8] Hyndman, J. J.: Strong duality of finite algebras that generate the same quasivariety. Algebra Universalis 51 (2004), 29-34. DOI 10.1007/s00012-004-1847-3 | MR 2067149 | Zbl 1092.08004
[9] Pitkethly, J. G., Davey, B. A.: Dualisability: Unary Algebras and Beyond. Springer (2005). MR 2161626 | Zbl 1085.08001
[10] Saramago, M.: Some remarks on dualisability and endodualisability. Algebra Universalis 43 (2000), 197-212. DOI 10.1007/s000120050153 | MR 1773938 | Zbl 1011.08003
[11] Saramago, M. J., Priestley, H. A.: Optimal natural dualities: the structure of failsets. Internat. J. Algebra Comput. 12 (2002), 407-436. DOI 10.1142/S0218196702000791 | MR 1910686 | Zbl 1027.08006
[12] Willard, R.: New tools for proving dualizability. Dualities, Interpretability and Ordered Structures (Lisbon, 1997). J. Vaz de Carvalho and I. Ferreirim Centro de Álgebra da Universidade de Lisboa (1999), 69-74.
[13] Zádori, L.: Natural duality via a finite set of relations. Bull. Austral. Math. Soc. 51 (1995), 469-478. DOI 10.1017/S0004972700014301 | MR 1331440
Partner of
EuDML logo