This is a preview of subscription content, log in via an institution to check access.
References
A. V. Kuznetsov, “The word problem and functional completeness of algebraic systems,” in: Proceedings of the 3 All-Union Mathematical Congress, [in Russian], Akad. Nauk SSSR, Moscow, 1956, pp. 145–146.
Á. Szendrei, Clones in Universal Algebra. Séminaire de Mathématique Supérieures (Seminar on Higher Mathematics;99), Les Presses de l'Université de Montreal, Montreal (1986).
E. L. Post, The Two- Valued Iterative Systems of Mathematical Logic, Princeton Univ. Press, Princeton (1941), (Ann. of Math. Stud.,5)
A. A. Krokhin, “Monoidal intervals in clone lattices,” Algebra i Logika,34, No. 3, 288–310 (1995).
A. A. Bulatov, A. A. Krokhin, K. L. Safin, and E. V. Sukhanov, “On the structure of clone lattices,” in: General Algebra and Discrete Mathematics, Heldermann Verlag, Berlin, 1995, pp. 27–34.
A. A. Krokhin, “On clones, transformation monoids, and associative rings,” Algebra Universalis,37, No. 4, 527–540 (1997).
A. A. Krokhin, “Boolean lattices as intervals in clone lattices,” Multiple-Valued Logic,2, No. 3, 263–271 (1997).
A. I. Mal'tsev, Iterative Post Algebras [in Russian], Nauka, Novosibirsk, 1976.
G. A. Burle, “Classes ofk-valued logic containing all functions of a certain variable,” Diskretnyî Analiz, No. 10, 3–7 (1967).
S. V. Yablonskiî, “Functional constructions ink-valued logic,” Trudy Mat. Inst. Steklov. Akad. Nauk SSSR,51, 5–142 (1958).
I. G. Rosenberg, “Über die funktionale Vollständigkeit in den mehrwerigen Logiken,” Pozpr. CSAV Rada Math. Prir. Ved. Praha,80, No. 4, 3–93 (1970).
J. Demetrovics and L. Hannák, “The number of reducts of a preprimal algebra,” Algebra Universalis,16, 178–185 (1983).
A. A. Salomaa, “On infinitely generated sets of operations in finite algebras,” Ann. Univ. Turku. Ser. AI,74, 1–12 (1964).
D. Lau, “Über die Anzahl von abgeschlossnen Mengen linearer Funktionen dern-wertigen Logik,” Elektron. Information. Kybernet.,14, No. 11, 561–563 (1978).
Á. Szendrei, “Algebras of prime cardinality with cyclic automorphism,” Arch. Math. (Basel), No. 39, 417–427 (1982).
L. Szabó and Á. Szendrei, “Slupecki-type criteria for quasilinear functions over a finite dimensional vector space,” Elektron. Information. Kybernet. 1981, V. 17, N 11-12. P. 601–611.
E. Yu. Zakharova, V. B. Kudryavtsev, and S. V. Yablonskiî, “On precomplete classes ink-valued logics,” Dokl. Akad. Nauk SSSR,186, 509–512 (1969).
L. Haddad and I. G. Rosenberg, “Finite clones containing all permutations,” Canad. J. Math.,46, No. 5, 951–970 (1994).
I. Ágoston, J. Demetrovics, and L. Hannák, “On the number of clones containing all constants,” Colloq. Math. Soc. János Bolyai, No. 43, 21–25 (1983). (Lectures in Universal Algebra.)
Á. Szendrei, “Term minimal algebras,” Algebra Universalis,32, No. 4, 439–477 (1994).
G. Rousseau, “Completeness in finite algebras with a single operation,” Proc. Amer. Math. Soc.,18, 1009–1013 (1967).
J. Demetrovics and L. Hannák, “Construction of large sets of clones,” Z. Math. Logik Grundlag. Math., No. 33, 127–133 (1987).
Á. Szendrei, “Short maximal chains in the lattice of clones over a finite set,” Math. Nachr., No. 110, 43–58 (1983).
Additional information
Ekaterinburg. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 3, pp. 619–631, May–June, 1999.
Rights and permissions
About this article
Cite this article
Krokhin, A.A. Maximal clones in monoidal intervals. I. Sib Math J 40, 528–538 (1999). https://doi.org/10.1007/BF02679760
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02679760