A certain Galois connection and weak automorphisms
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (1997)
- Volume: 36, Issue: 1, page 15-26
- ISSN: 0231-9721
Access Full Article
topHow to cite
topGłazek, Kazimierz. "A certain Galois connection and weak automorphisms." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 36.1 (1997): 15-26. <http://eudml.org/doc/23646>.
@article{Głazek1997,
author = {Głazek, Kazimierz},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {iterative Post algebra; Galois connection; survey; weak automorphisms; families of operations},
language = {eng},
number = {1},
pages = {15-26},
publisher = {Palacký University Olomouc},
title = {A certain Galois connection and weak automorphisms},
url = {http://eudml.org/doc/23646},
volume = {36},
year = {1997},
}
TY - JOUR
AU - Głazek, Kazimierz
TI - A certain Galois connection and weak automorphisms
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 1997
PB - Palacký University Olomouc
VL - 36
IS - 1
SP - 15
EP - 26
LA - eng
KW - iterative Post algebra; Galois connection; survey; weak automorphisms; families of operations
UR - http://eudml.org/doc/23646
ER -
References
top- Aczél J., On mean values, Bull. Amer. Math. Soc. 54 (1948), 392-400. (1948) Zbl0030.02702MR0024482
- Aczél J., Sur les opérations définies pour nombres réels, Bull. Soc. Math. France 76 (1949), 59-64. (1949) MR0029946
- Aczél J., Vorlesungen über Funktionalgleichungen und ihre Anwendungen, Birkhäuser Verlag, Basel, 1961. (1961) Zbl0096.09102MR0124647
- Aczél J., Lecture on Functional Equations and Their Applications, Academic Press, New York, 1966. (1966) MR0208210
- Aczél J., On Applications and Theory of Functional Equations, Birkhäuser Verlag, Basel, 1969. (1969) Zbl0176.12801MR0240491
- Aczél J., Wagner C., A characterization of weighted arithmetical means, SIAM J. Algebraic Discrete Methods 1 (1980), 256-260. (1980) MR0586152
- Bairamov R. A., On completeness problem in iterative Post algebras, Special Topics in Algebra and Topology (in Russian) 1 (1980), 1-27. (1980)
- Bairamov R. A., Some new results in the theory of function algebras of finite-valued logics, In: Colloq. Math. Soc. J. Bolyai, 28 (Finite Algebra and Multiple-Valued Logic), North-Holland, Amsterdam, 1981, 41-67. (1981) Zbl0485.03035MR0648607
- Birkhoff G., Lattice Theory, (1st edition), Amer. Math. Soc., Providence, R. I., 1940. (1940) Zbl0063.00402MR0001959
- Birkhoff G., Lattice Theory, (3rd edition), Amer. Math. Soc., New York, N. Y., 1967. (1967) Zbl0153.02501MR0227053
- Birkhoff G., The role of modern algebra in computing, In: Computers in algebra and number theory, SIAM-AMS Proc., IV, Providence, R. I., 1971, 1-47. (1971) Zbl0241.68003MR0378453
- Birkhoff G., Some applications of universal algebra, In: Colloq. Math. Soc. J. Bolyai, 29 (Universal Algebra), North-Holland, Amsterdam, 1982, 107-128. (1982) Zbl0519.03049MR0660852
- Carlitz L., Permutation in finite fields, Acta Sci. Math. (Szeged) 24 (1963), 196-203. (1963) MR0156838
- Cohn P. M., Universal Algebra, Harper & Row, New York, 1965 (second edition, D. Reidel Publ. Co., Dordrecht, 1981). (1965) Zbl0141.01002MR0620952
- Demetrovics J., Hannák L., On the cardinality of self-dual closed classes in k-valued logics, Közl. MTA Számitástech. Automat. Kutató Int., Budapest 23 (1979), 7-17. (1979) MR0544438
- Demetrovics J., Hannák L., Marčenkov S. S., On closed classes of self-dual functions in , In: Colloq. Math. Soc. J. Bolyai, 28 (Finite Algebra and Multiple-Valued Logic), North-Holland, Amsterdam, 1981, 183-189. (1981) MR0648615
- Demetrovics J., Hannák L., Rónyai L., Selfdual classes and automorphism groups, In: Proceedings of the 13th International Symposium on Multiple-Valued Logic (May 23-25, 1983, Kyoto), IEEE Comput. Soc., New York, 1983, 122-125. (1983) Zbl0559.03041
- Demetrovics J., Rónyai L., On free spectra of clones with sharply transitive automorphism groups, In: Proceedings of the 13th International Symposium on Multiple-Valued Logic (May 23-25, 1983, Kyoto), IEEE Comput. Soc., New York, 1983, 126-128. (1983) Zbl0559.03042MR0784583
- Demetrovics J., Rónyai L., On free spectral of self-dual clones, , Math. Structures-Comput. Math-Math. Modelling 2 (1984), 136-140. (1984) MR0790873
- Dudek J., Płonka E., Weak automorphisms of linear spaces, Colloq. Math. 22 (1971), 201-208. (1971) Zbl0335.08009MR0280428
- Evans T., Some remarks on the general theory of clones, In: Colloq. Math. Soc. J. Bolyai, 28 (Finite Algebra and Multiple-Valued Logic), North-Holland, Amsterdam, 1981, 203-244. (1981) Zbl0485.08003MR0648617
- Evans T., Embedding and representation theorems for clones and varieties, Bull. Austral. Math. Soc. 40 (1989), 199-205. (1989) Zbl0686.08004MR1012828
- Evans T., Hardy L., Sheffer stroke function in many-valued logics, Portugal. Math. 16 (1957), 83-93. (1957) MR0102478
- de Finetti B., Sul concetto di media, Giornale di Istituto di Attuarii 2 (1931). (1931) Zbl0002.27802
- Foster A. L., The idempotent elements of a commutative ring form a Boolean algebra: Ring-duality and transformation theory, Duke Math. J. 12 (1945), 143-152. (1945) Zbl0060.06603MR0012264
- Foster A. L., On n-ality theories in rings and their logical algebras, including tri-ality principle in three-valued logics, Amer. J. Math. 72 (1950), 101-123. (1950) MR0033278
- Foster A. L. Bernstein B. A., Symmetric approach to commutative rings with duality theorem: Boolean duality as special case, Duke Math. J. 11 (1944), 603-616. (1944) MR0010545
- Foster A. L., Bernstein B. A., A dual-symmetric definition of fields, Amer. J. Math. 67 (1945), 329-349. (1945) MR0012275
- Głazek K., Weak automorphisms of integral domains, Colloq. Math. 22 (1970), 41-49. (1970) Zbl0211.32103MR0272698
- Głazek K., On weak automorphisms of finite fields, In: Colloq. Math. Soc. J. Bolyai, 28 (Finite Algebra and Multiple-Valued Logic), North-Holland, Amsterdam, 1981, 275-300. (1981) Zbl0487.12012MR0648620
- Głazek K., Weak automorphisms and some Galois connection, In: Abstracts of Short Communications, International Congress of Mathematicians, Kyoto (Japan) 1990, 11. (1990)
- Głazek K., On weak automorphisms of some finite algebras, Contemp. Math. 131 (1992), 99-110. (1992) Zbl0785.08001MR1175875
- Głazek K., Morphisms of general algebras without fixed fundamental operations, In: General Algebra and Applications, Heldermann Verlag, Berlin, 1993, 89-112. (1993) Zbl0793.08006MR1209889
- Głazek K., Algebras of Algebraic Operations and Morphisms of Algebraic Systems, Acta Univ. Wratislaviensis 1602, Wyd. Uniw. Wrocławskiego, Wrocław, 1994 (Polish). (1994) Zbl0817.08001MR1323430
- Goetz A., On weak isomorphisms and weak homomorphisms of abstract algebras, Colloq. Math. 14 (1966), 163-167. (1966) Zbl0192.09504MR0184889
- Gorlov V. V., Lau D., Über Automorphismen auf Funktionenalgebren, Rostock Math. Kolloq. 23 (1983), 35-42. (1983) Zbl0528.03037MR0729479
- Hinrichs L. A., Niven I., van den Eynden C. J., Fields defined by polynomials, Pacific J. Math. 14 (1964), 537-545. (1964) MR0162790
- Hosszú M., On the functional equation of autodistributivity, Publ. Math. (Debrecen) 3 (1953-1954), 83-86. (1953) MR0062331
- Hosszú M., Some functional equations related with the associative law, Publ. Math. (Debrecen) 3 (1954), 205-214. (1954) Zbl0058.10803MR0072147
- Huntington E. V., A set of postulates for ordinary complex algebra, Trans. Amer. Math. Soc. 6 (1905), 209-229. (1905) MR1500708
- Kalman D., Turner P., Algebraic structures with exotic operations, Internat. J. Math. Ed. Sci. Tech. 10 (1979), 173-174. (1979)
- Kitagawa T., On some class of weighted means, Proc. Physico-Math. Soc. of Japan 16 (1934). (1934) Zbl0009.05806
- Knaster B., Sur une équivalence pour les fonctions, Colloq. Math. 2 (1949), 1-4. (1949) Zbl0038.04203MR0038382
- Kolmogoroff A., Sur la notion de la moyenne, Atti Accad. Naz. Lincei, Rendiconti (6) 12 (1930), 388-391. (1930)
- Lau D., Automorphismen auf den maximallen Klassen der k-wertigen Logik, Rostock. Math. Kolloq. 12 (1979), 13-16. (1979) MR0554690
- Lausch H., Nöbauer W., Algebra of Polynomials, North-Holland, Amsterdam, 1973. (1973) Zbl0283.12101MR0349544
- Lazard M., Lois de groupes et analyseurs, Ann. Sci. École Norm. Sup. (3) 72 (1955), 4, 299-400. (1955) Zbl0068.02702MR0077542
- Lazard M., Commutative Formal Groups, Lecture Notes in Math. 443, Springer-Verlag, Berlin, 1975. (1975) Zbl0304.14027MR0393050
- Leight V., Self-dual sets of unary and binary connectives for 3-valued propositional calculus, Z. Math. Logik Grundlag. Math. 18 (1972), 201-204. (1972) MR0424519
- Levit R. J., Fields in terms of a single operation, Trans. Amer. Math. Soc. 57 (1945), 426-440. (1945) Zbl0060.08208MR0012274
- Lidl R., Niederreiter H., Finite Fields, Addison-Wesley Publ. Co., London, 1983. (1983) Zbl0554.12010MR0746963
- Lyndon R. C, Identities in two-valued calculi, Trans. Amer. Math. Soc. 71 (1951), 457-465. (1951) Zbl0044.00201MR0044470
- Mal’cev A. I., Iterative algebras and Post’s varieties, Algebra i Logika 5 (1966), 5-24 (in Russian). (1966) MR0207609
- Mal’cev A. I., Iterative Post’s algebra, Novosibir. Gos. Univ., Novosibirsk, 1976 (in Russian). (1976) MR0469754
- Mal’cev I. A., Congruences and automorphisms on the cells of Post algebras, Algebra i Logika 11 (1972), 315-325 (in Russian). (1972) MR0327514
- Marčenkov S. S., Closed classes of self-dual functions of many-valued logic, Problemy Kibernet. 36 (1979), 5-22, 279 (in Russian). (1979) MR0568444
- Marčenkov S. S., On the classification of algebras whose automorphisms group is the alternating group, Dokl. Akad. Nauk SSSR 265 (1982), 533-536 (in Russian). (1982) MR0665319
- Marčenkov S. S., Demitrovics J., Hannák L., Closed classes of self-dual functions in , Metody Diskret. Analiz. 34 (1980), 38-73 (in Russian). (1980) MR0625383
- McKenzie R. N., McNulty G. F., Taylor W.F., Algebras, Lattices, Varieties, Wadsworth and Brooks, Monterey, Cal., v. I, 1987. (1987) Zbl0611.08001
- Menger K., General algebra of analysis, Repts. Math. Colloq., Notre Dame Univ. 7 (1946), 49-60. (1946) Zbl0060.06609MR0016743
- Menger K., The algebra of functions: Past, present, future, Rend. Mat. Appl. 20 (1961), 409-430. (1961) Zbl0113.03904MR0141618
- Miyakawa M., Functional completeness and structure of three-valued logic I-Classification of , Researches of the Electronical Laboratory 717, Tokyo, Japan, 1971. (1971)
- Mullin A. A., Selfdual symmetric switching functions with a certain number of constraints, IRE Trans, EC-(84), Dec. 1959, 498-499. (1959)
- Nagumo M., Über eine Klasse der Mittelwerte, Japon. J. Math. 7 (1930), 71-79. (1930)
- Nöbauer W., Über die Automorphismen von Kompositionsalgebren, Acta Math. Acad. Sci. Hungar. 26 (1975), 275-278. (1975) Zbl0321.08003MR0389721
- Ore O., Galois connexions, Trans. Amer. Math. Soc. 55 (1944), 493-513. (1944) Zbl0060.06204MR0010555
- Pöschel R., Cryptomorphisms of non-indexed algebras and relational systems, In: Colloq. Math. Soc. J. Bolyai, 43 (Lectures in Universal Algebra), North-Holland, Amsterdam 1985, 365-404. (1985) MR0860274
- Pöschel R., Kaluznin (Kaloujnine) L. A., Funktionen- und Relationen-algebren, Deutscher Verl. d. Wissenschaften, Berlin, 1979. (1979) MR0543839
- Post E. L., Determination of all closed systems of truth tables, Bull. Amer. Math. Soc. 26 (1920), 437. (1920)
- Post E. L., Two-valued iterative systems of mathematical logic, Princeton Univ. Press, Princeton, 1941. (1941) Zbl0063.06326MR0004195
- Rickart, C E., One-to-one mappings of rings and lattices, Bull. Amer. Math. Soc. 54 (1948), 758-764. (1948) Zbl0032.24904MR0026039
- Rose A., Self-dual binary and ternary connectives for m-valued logic, Math. Ann. 143 (1961), 448-462. (1961) MR0123471
- Ryll-Nardzewski C., Sur les moyennes, Studia Math. 11 (1949), 31-37. (1949) MR0035792
- Schein B. M., Trohimenko V. S., Algebras of multiplace functions, Semigroup Forum 17 (1979), 1-64. (1979) Zbl0397.08001MR0521147
- Senft J. R., On weak automorphisms of universal algebras, Dissertationes Math. (Rozprawy Mat.) 74 (1970), 1-35. (1970) Zbl0231.08006MR0274377
- Stojmenović I., Classification of a maximal clone of three-valued logical functions, J.Inform. Process. Cybernet. EIK 22 (1986), 533-545. (1986) Zbl0612.94014MR0908969
- Stojmenović I., Miyakawa M., On symmetric self-dual functions in many-valued logics, (preprint Univ. Novi Sad, Yugoslavia, 1986). (1986)
- Szendrei Á., Clones in Universal Algebra, Les Presses de l’Universite de Montréal, Montréal, 1986. (1986) Zbl0603.08004MR0859550
- Vincze E., Über die Charakterisierung der assoziativen Funktionen von mehreren Veränderlichen, Publ. Math. (Debrecen), 6 (1959), 241-253. (1959) Zbl0091.11802MR0111952
- Vincze E., Verallgemeinerung eines Satzes über assoziative Funktionen von mehreren Veränderlichen, Publ. Math. (Debrecen) 8 (1961), 68-74. (1961) Zbl0102.11101MR0132941
- Whitlock H. J., A composition algebra for multiplace functions, Math. Ann. 157 (1964), 167-178. (1964) Zbl0126.03501MR0173647
- Yablonskii S. V., Functional construction in the k-valued logic, Trudy Mat. Inst. Steklov. 51 (1958), 5-142 (in Russian). (1958) MR0104578
- Yablonskii S. V., Gavrilov G. P., Kudryavcev V. B., Functions of the algebra of logic and Post classes, Izd. Nauka, Moskva, 1966 (in Russian). (1966) MR0215649
- Yaqub A., On the theory of ring-logics, Canad. J. Math. 8 (1956), 323-328. (1956) Zbl0073.02201MR0078970
- Zariski O., Samuel P., Commutative Algebra, van Nostrand, Princeton, N. J., v. I, 1958. (1958) Zbl0081.26501MR0090581
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.