On clones determined by their initial segments
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 49 (2008) no. 3, pp. 209-227.
@article{CTGDC_2008__49_3_209_0,
     author = {Sichler, J. and Trnkov\'a, V\v{e}ra},
     title = {On clones determined by their initial segments},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {209--227},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {49},
     number = {3},
     year = {2008},
     zbl = {1163.08001},
     mrnumber = {2449674},
     language = {en},
     url = {http://archive.numdam.org/item/CTGDC_2008__49_3_209_0/}
}
Sichler, J.; Trnková, V. On clones determined by their initial segments. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 49 (2008) no. 3, pp. 209-227. http://archive.numdam.org/item/CTGDC_2008__49_3_209_0/

[1] J. Adámek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York. | MR 1051419 | Zbl 0695.18001

[2] J. T. Baldwin and J. Berman, Elementary classes of varieties, Houston. J. Math. 7 (1981),473-492. | MR 658563 | Zbl 0487.08007

[3] P. M. Cohn, Universal Algebra, Harper and Row, New York, 1965. | MR 175948 | Zbl 0141.01002

[4] G. Grätzer, Universal Algebra, Second Edition, Springer-Verlag, New York, 1979. | MR 538623

[5] P. Hall, Some word problems, J. London Math. Soc. 33 (1958), 482-496. | MR 102540 | Zbl 0198.02902

[6] F. W. Lawvere, Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869-872. | MR 158921 | Zbl 0119.25901

[7] F. W. Lawvere, Some algebraic pwblems in the context of functorial semantics of algebraic theories, Lect. N. in Math., vol. 61, Springer-Verlag, Berlin and New York, 1968, pp. 41-46. | MR 231882 | Zbl 0204.33802

[8] K. D. Magill, The semigroup of endomorphisms of a Boolean ring, Semigroup Forum 4 (1972),411-416. | MR 272690 | Zbl 0224.06007

[9] K. D. Magill, A survey of semigroups of continuons selfmaps, Semigroup Forum 11 ( 1975/76), 189-282. | MR 393330 | Zbl 0338.20088

[10] C. J. Maxson, On semigroups of Boolean ring endomorphisms, Semigroup Forum 4 (1972), 78-82. | MR 297900 | Zbl 0262.06011

[11] R. N. Mckenzie, G. F. Mcnulty and W. F. Taylor, Algebras, Lattices, Varieties, Volume 1, Wadsworth & Brooks/Cole, Monterey, California, 1987. | Zbl 0611.08001

[12] R. N. Mckenzie and C. Tsinakis, On recovering of a bounded distributive lattice from its endomorphism monoid, Houston J. Math 7 (1981), 525-529. | MR 658568 | Zbl 0492.06009

[13] E. L. Post, Introduction to a general theory of elementary propositions, Amer. J. Math. 43 (1921), 163-185. | JFM 48.1122.01 | MR 1506440

[14] E. L. Post, The Two-valued Iterative Systems of Mathematical Logic, Annals of Mathematics Studies No. 5, Princeton University Press, Princeton, N. J., 1941. | MR 4195 | Zbl 0063.06326

[15] B. M. Schein, Ordered sets, semilattices, distributive lattices and Boolean algebras with homomorphic endomorphism semigroups, Fund. Math. 68 (1970), 31-50. | MR 272686 | Zbl 0197.28902

[16] J. Sichler and V. Trnková, Clones in topology and algebra, Acta Math. Univ. Comenianae 66 (1997), 243-260. | MR 1620417 | Zbl 0970.08004

[17] J. Sichler and V. Trnková, Clone segment independence in topology and algebra, Acta Sci. Math. (Szeged) 68 (2002), 611-672. | MR 1954539 | Zbl 1017.54006

[18] Á. Szendrei, Clones in Universal Algebra, Les Presses de L'Université de Montréal, 1986. | MR 859550 | Zbl 0603.08004

[19] W. Taylor, The Clone of a Topological Space, Research and Exposition in Mathematics, vol. 13, 1986, Heldermann Verlag, 1986. | MR 879120 | Zbl 0615.54013

[20] V. Trnková, Representability and local representability of algebraic theories, Algebra Universalis 29 (1998), 121-144. | MR 1636983 | Zbl 0936.18007

[21] V. Trnková and J. Sichler, All clones are centralizer clones, preprint (2007). | MR 2551786 | Zbl 1201.03017

J. Sichler, Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2, sichler@cc.umanitoba.ca

V. Trnková, Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic, trnkova@karlin.mff.cuni.cz