This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Andréka,H.; Burmeister,P.; Németi,I., Quasivarieties of partial algebras-A unified approach towards a two-valued model theory for partial algebras. Preprint No.557, Techn.Hochschule Darmstadt, July 1980.
Birkhoff, G., Frink, O., Representation of lattices by sets. Trans.Am.Math. Soc. 64 (1948), 299–316. MR10 #279.
Bodnarčuk, V.G.; Kalužnin, L.A.; Kotov,V.N.; Romov,B.A., Galois theory for Post algebras. (Russian) Kibernetika (Kiev) Part I:3 (1969) 1–10; Part II:5 (1969) 1–9. English translation Cybernetics 5 (1969) 243–252, 531–539, MR46 #55.
Fleischer, I.; Rosenberg, I.G., The Galois connection between partial functions and relations. Pacific J.Math. 79 No.1 (1978) 93–98.
Freivald, R.V., Completeness criteria for partial functions of the algebra of logic and many-valued logics.(Russian) Dokl.Akad.Nauk SSSR 167 No.6 (1966) 1249–1250.
Freivald,R.V., Functional completeness for not everywhere defined functions of the algebra of logic.(Russian) Diskret.Analiz, Novosibirsk, No.8 (1966) 55–68.
Geiger, D. Closed systems of functions and predicates. Pacific J.Math. 27 No.1 (1968) 95–100. MR38 #3207.
Grätzer, G., Universal algebra. D. Van Nostrand 1968; 2nd ed., Springer-Verlag, New York 1979.
Iskander, A.A., Subalgebra systems of powers of partial universal algebras. Pacific J.Math. 38 (1971) 457–463. MR46 #5212.
Janov, Ju.I.; Mučnik, A.A., Existence of k-valued closed classes without a finite basis. (Russian) Dokl.Akad.Nauk SSSR 127 (1959) 44–46. MR21 #7174.
Kalužnin, L.A., Klin, M.H., Certain subgroups of symmetric and alternating groups. (Russian) Math.USSR-Sb 16 (1972) 95–124, MR45 #6906.
Krasner, M., Remarque au sujet de "Une generalisation de la notion de corps", Journ.de Math. (1938) 367–385. J.Math.Pures Appl. 18 (1939) 417–418, MR1 p.198
Krasner,M., Generalisation abstraite de la theorie de Galois. Colloques internationaux du Centre National R.S. XXIV 1949, Paris. Algèbre et théorie des nombres, 163–165, Paris, CNRS, 1950, MR12 p. 796.
Krasner,M., Generalisation abstraite de la théorie de Galois. Proceedings of the International Congress of Mathematics 1950, Cambridge Vol.1, pp.331–332, Providence AMS 1952.
Krasner,M., Endotheorie de Galois abstraite. Congres international des mathématiciens, Moscou, 1966, Résumés 2, Algèbre p.61, Moscou ICM 1966.
Krasner,M., Endotheorie de Galois abstraite. Seminaire P.Dubreil, M.L.Dubreil, L.Lesieur et C.Pisot (Algèbre et théorie des nombres) 22ieme annee, Fasc.1, 1968/69, no.6 (19 pages) MR44 #45.
Krasner, M., Endotheorie de Galois abstraite et son théorème d'homomorphie. C.R.Acad.Sci.Paris 282 (1976) 683–686.
Krasner,M., Abstract Galois theory and endotheory. Manuscript Paris 1980.
Kuznecov,A.V. Forty years of Soviet Mathematics (Russian) T.1, p.102–115, Moscou 1957.
Mal'cev, A.I. Iterative algebras and Post's varieties (Russian). Algebra i Logika 5 (1966) 5–24. English translation: Mal'cev, The metamathematics of algebraic systems, pp.396–415, North-Holland 1971.
Murskii, V.L., The existence in the three-valued logic of a class with a finite basis having no finite basis of identities (Russian). Doklady Akad. Nauk.SSSR 163 (1965) 815–818. MR 32 #3998.
Pöschel, R., Postsche Algebren von Funktionen uber einer Famille endlicher Mengen. Z.Math.Logik Grundlagen Math. 19 (1973) 37–74.
Pöschel, R.; Kalužnin, L.A., Funktionen und Relationenalgebren. Math.Monographien 15 VEB Deutscher Verlag d. Wissenschaften Berlin 1979 and Math.Reihe B.67. Birkhäuser Verlag Basel,Stuttgart 1979.
Romov,B.A., Local characteristics of Post algebras.(Russian) Part I: Kibernetika (Kiev) No.5 (1976) 38–45. Part II: ibid No.1 (1977) 12–20. English translation: Cybernetics (1977).
Romov,B.A., The Galois correspondence between Post's iterative algebras and relations on an infinite set. (Russian) ibid No.3 (1977) 62–64. English translation: Cybernetics (1977).
Romov,B.A., The algebra of partial functions and their invariants. (Russian) ibid no.2 March–April 1981, 1–11. English translation: Cybernetics (1981) 157–167.
Post,E., The two valued iterative systems of mathematical logic. Annals of Math.Studies 5, Princeton 1951.
Rosenberg, I.G., La structure des fonctions de plusieurs variables sur un ensemble fini. C.R.Acad.Sci.Paris. Ser.A–B 260 (1965) 3817–3819. MR31 #1185.
Rosenberg, I.G., Uber die funktionale Vollständigkeit in der mehrwertigen Logiken. Rozpravy Českolovenské Akad.Věd., Řada Mat.Přír.Věd. 80, 4 (1970) 1–93. MR45 #1732.
Rosenberg, I.G., Algebren und Relationen. Elektron. Informationsverarbeitung Kybernetik 6 (1970) 115–124, MR42 #48.
Rosenberg, I.G., A classification of universal algebras by infinitary relations, Algebra Universalis 1 (1972) 350–354. MR45 #6732.
Rosenberg, I.G., Universal algebras with all operations of bounded range. Colloq.Math. 30, Fasc.2 (1974) 177–185.
Rosenberg, I.G., Special types of universal algebras preserving a relation. Portugaliae Math. Vol. 34 Fasc.3 (1975) 174–188.
Rosenberg,I.G., Functional completeness in heterogeneous multiple-valued logics Proc.1975 Int.Symp.on Multiple-Valued Logics, 36–44. Bloomington, Ind. 1975.
Rosenberg, I.G., The set of maximal closed classes of operations on an infinite set A has card 22A. Archiv.d.Math. 27 (1976) 561–568.
Rosenberg, I.G., Completeness properties of multiple-valued logic algebras. In Computer Science and Multiple-Valued Logic, Theory and Applications (D.C. Rine, ed.) North-Holland, Amsterdam-New York-Oxford 1977, 144–186.
Rosenberg, I.G., Subalgebra systems of direct powers. Algebra Universalis 8/2 (1978) 221–227.
Rosenberg,I.G., On a Galois connection between algebras and relations and its applications. Contributions to general algebra (Proc. of the Klagenfurt conference 1978; H.Kautschitsch,W.B., Müller,W., Nöbauer,eds.) Verlag J.Heyn Klagenfurt 1979, 273–289.
Rosenberg,I.G., Clones containing the direct square of a primal algebra. Proc. 12th Intern.Symposium Multiple-valued Logic. CNAM Paris (1982) 30–34.
Rosenberg,I.G., Szendrei,Á., Submaximal clones with a prime order automorphism, CRMA-732, Montreal 1981 (20p.) submitted.
Sauer, N., Stone, M.G., The algebraic closure of a semigroup of functions. Algebra Universalis 7 (1977) 219–233.
Sauer, N., Stone, M.G., A Galois correspondence between algebras and endomorphisms, Colloq.Math.Soc.J. Bolyai 29 (1977) 691–695.
Słominski, J., On mappings between quasi-algebras. Coll.Math. 21 (1970), 5–21.
Szabó, L., Concrete representation of related structures of universal algebras. Acta Sci.Math. (Szeged) 40 (1978) 175–184.
Werner, H., Which partition lattices are congruence lattices, Colloq.Math.Soc.J. Bolyai 14 (1974), 433–453.
Wojdyło, B., Remarks on lattices of congruences relations of quasialgebras. Coll.Math. 27 (1973) 187–191.
Burmeister,P., Wojdyło,B., Properties of homomorphisms and quomorphisms. Preprint No. 657, Technische Hochschule Darmstadt 1982 (26 p.)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Rosenberg, I.G. (1983). Galois theory for partial algebras. In: Freese, R.S., Garcia, O.C. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063443
Download citation
DOI: https://doi.org/10.1007/BFb0063443
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12329-3
Online ISBN: 978-3-540-40954-0
eBook Packages: Springer Book Archive
