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Tytuł książki

Distributive multisemilattices

Autorzy

Arthur Knoebel Anna Romanowska

Seria

Rozprawy Matematyczne tom/nr w serii: 309 wydano: 1991

Zawartość

Pełne teksty: http://matwbn.icm.edu.pl/ksiazki/rm/rm309/rm30901.pdf [zdalny]

Warianty tytułu

Abstrakty

EN

CONTENTS
1. Introduction........................................................................................................................5
2. Definition, basic examples and properties of multisemilattices...........................................6
3. The subdirectly irreducibles..............................................................................................13
4. The lattice of subvarieties of $D_n$.................................................................................18
5. Subvarieties of $D_n$ defined by identities involving at most two operation symbols......24
6. Some further comments and open problems....................................................................34
References...........................................................................................................................40

Słowa kluczowe

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 309

Liczba stron

42

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCIX

Daty

wydano
1991
otrzymano
1990-05-31

Twórcy

autor
Arthur Knoebel
  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.
autor
Anna Romanowska
  • Institute of Mathematics, Warsaw Technical University, 00-661 Warszawa, Poland

Bibliografia

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  • [BK] G. Birkhoff and S. A. Kiss, A ternary operation in distributive lattices, ibid. 53 (1947), 749-752.
  • [C] P. M. Cohn, Universal Algebra, Reidel, Dordrecht 1981.
  • [D1] J. Dudek, On bisemilattices I, Colloq. Math. 47 (1982), 1-5.
  • [D2] J. Dudek, On bisemilattices II, to appear.
  • [D3] J. Dudek, On bisemilattices III, Math. Sem. Notes Kobe Univ. 10 (1982), 275-279.
  • [DG] J. Dudek and E. Graczyńska, The lattice of varieties of algebras, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 337-340.
  • [DR] J. Dudek and A. Romanowska, Bisemilattices with four essentially binary polynomials, in: Colloq. Math. Soc. J. Bolyai 33, North-Holland, 1983, 337-360.
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  • [G2] J. Gałuszka, On bisemilattices with generalized absorption laws, I, Demonstratio Math. 20 (1987), 37-43.
  • [G3] J. Gałuszka, Bisemilattices with five essentially binary polynomials, Math. Slovaca 38 (1988), 123-132.
  • [GR] G. Gierz and A. Romanowska, Duality for distributive bisemilattices, J. Austral. Math. Soc., to appear.
  • [Gi] M. Ginsberg, Bilattices, preprint, Dept. of Computer Science, Stanford University, 1986.
  • [Go1] R. Godowski, On bisemilattices with one absorption law, Demonstratio Math. 19 (1986), 304-318.
  • [Go2] R. Godowski, On bisemilattices with co-absorption law, preprint.
  • [Gr1] G. Grätzer, General Lattice Theory, Akademie-Verlag, Berlin 1978.
  • [Gr2] G. Grätzer, Universal Algebra, 2nd ed., Springer, New York 1979.
  • [Gra] A. A. Grau, Ternary Operations and Boolean Algebra, Ph.D. Thesis, Univ. of Michigan, 1944.
  • [H] T. J. Head, The varieties of commutative monoids, Nieuw Arch. Wisk. 16 (1968), 203-206.
  • [JK1] J. Jakubík and M. Kolibiar, On some properties of a pair of lattices, Czechoslovak Math. J. 4 (79) (1954), 1-27 (in Russian).
  • [JK2] J. Jakubík and M. Kolibiar, Lattices with a third distributive operation, Math. Slovaca 27 (1977), 287-292.
  • [J] B. Jónsson, Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110-121.
  • [K] J. A. Kalman, Subdirect decomposition of distributive quasilattices, Fund. Math. 71 (1971), 161-163.
  • [Ki] A. Kisielewicz, A solution of Dedekind's problem on the number of isotone Boolean functions, J. Reine Angew. Math. 3 (1988), 1-6.
  • [Kn1] A. Knoebel, A comment on Balbes' representation theorem for distributive quasi-lattices, Fund. Math. 90 (1976), 187-188.
  • [Kn2] A. Knoebel, The equational classes generated by single functionally precomplete algebras, Mem. Amer. Math. Soc. 57 (332) (1985).
  • [Kn3] A. Knoebel, Distributive polylattices, Abstracts Amer. Math. Soc. 7 (1986), 19.
  • [LPP] H. Lakser, R. Padmanabhan and C. R. Platt, Subdirect decomposition of Płonka sums, Duke Math. J. 39 (1972), 485-488.
  • [M1] A. I. Mal'cev, Algebraic Systems, Springer, Berlin 1973.
  • [M2] A. I. Mal'cev, Multiplication of classes of algebraic systems, Sibirsk. Mat. Zh. 8 (1967), 346-365 (in Russian).
  • [MMT] R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties, Wadsworth & Brooks/Cole, Monterey, Cal., 1987.
  • [MR] R. McKenzie and A. Romanowska, Varieties of ·-distributive bisemilattices, in: Contributions to General Algebra, Proc. Klagenfurt Conference 1978, Verlag Johannes Heyn, 1978, 213-218.
  • [Me] G. C. Meletiou, Linear spaces as distributive k-quasilattices, Demonstratio Math., to appear.
  • [N] J. Nieminen, Ideals in distributive quasi-lattices, Studia Univ. Babeş-Bolyai Math. 1977 (1), 6-11.
  • [Pa] R. Padmanabhan, Regular identities in lattices, Trans. Amer. Math. Soc. 158 (1971), 179-188.
  • [Pn] F. Pastijn, Idempotent distributive semirings II, Semigroup Forum 26 (1983), 151-166.
  • [PR] F. Pastijn and A. Romanowska, Idempotent distributive semirings I, Acta Sci. Math. (Szeged) 44 (1982), 239-253.
  • [P1] J. Płonka, On distributive quasi-lattices, Fund. Math. 60 (1967), 191-200.
  • [P2] J. Płonka, On a method of construction of abstract algebras, ibid. 61 (1967), 183-189.
  • [P3] J. Płonka, On distributive n-lattices and n-quasilattices, ibid. 62 (1968), 293-300.
  • [P4] J. Płonka, On equational classes of abstract algebras defined by regular equations, ibid. 64 (1969), 241-247.
  • [P5] J. Płonka, On free algebras and algebraic decompositions of algebras from some equational classes defined by regular equations, Algebra Universalis 1 (1971), 261-267.
  • [R1] A. Romanowska, On free algebras in some equational classes defined by regular equations, Demonstratio Math. 11 (1978), 1131-1137.
  • [R2] A. Romanowska, On bisemilattices with one distributive law, Algebra Universalis 10 (1980), 36-47.
  • [R3] A. Romanowska, Subdirectly irreducible ·-distributive bisemilattices, I, Demonstratio Math. 13 (1980), 767-785.
  • [R4] A. Romanowska, Free bisemilattices with one distributive law, ibid., 565-572.
  • [R5] A. Romanowska, Idempotent distributive semirings with a semilattice reduct, Math. Japon. 27 (1982), 483-493.
  • [R6] A. Romanowska, Free idempotent distributive semirings with a semilattice reduct, ibid., 467-481.
  • [R7] A. Romanowska, On algebras of functions from partially ordered sets into distributive lattices, in: Lecture Notes in Math. 1004, Springer, 1983, 245-256.
  • [R8] A. Romanowska, Building bisemilattices from lattices and semilattices, in: Contributions to General Algebra 2, Proc. Klagenfurt Conference 1982, Verlag Hölder-Pichler-Tempsky, 1983, 343-358.
  • [R9] A. Romanowska, On some constructions of bisemilattices, Demonstratio Math. 17 (1984), 1011-1021.
  • [R10] A. Romanowska, Constructing and reconstructing of algebras, ibid. 18 (1985), 209-230.
  • [R11] A. Romanowska, On regular and regularized varieties, Algebra Universalis 23 (1986), 215-241.
  • [RS1] A. Romanowska and J. D. H. Smith, Bisemilattices of subsemilattices, J. Algebra 70 (1981), 78-88.
  • [RS2] A. Romanowska and J. D. H. Smith, Distributive lattices, generalisations, and related non-associative structures, Houston J. Math. 11 (1985), 367-383.
  • [RS3] A. Romanowska and J. D. H. Smith, Model Theory, and Algebraic Approach to Order, Geometry and Convexity, Heldermann, Berlin 1985.
  • [RS4] A. Romanowska and J. D. H. Smith, On the structure of semilattice sums, preprint, 1987.
  • [RT] A. Romanowska and A. Trakul, On the structure of some bilattices, in: Universal and Applied Algebras, Proc. Universal Algebra Symposium, Turawa 1988, K. Halkowska and B. Stawski (eds.), World Scientific, Singapore 1989, 235-253.
  • [S] B. M. Schein, Homomorphisms and subdirect decompositions of semigroups, Pacific J. Math. 17 (1966), 529-547.
  • [T] A. Trakul, Bilattices, Master thesis, Warsaw Technical University, 1988 (in Polish).
  • [W] R. O. Winder, Threshold Logic, Ph.D. Thesis, Princeton Univ., 1962.

Języki publikacji

EN

Uwagi

1985 Mathematics Subject Classification: Primary 06A12, 08B15; Secondary 05C40, 08B05.

Identyfikator YADDA

bwmeta1.element.zamlynska-553ea7ba-6a08-4b20-8ee7-4c4ed1ce33b2

Identyfikatory

ISBN
83-85116-09-5
ISSN
0012-3862

Kolekcja

DML-PL
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