A construction for pseudocomplemented semilattices and two applications
HTML articles powered by AMS MathViewer
- by M. E. Adams and Matthew Gould
- Proc. Amer. Math. Soc. 106 (1989), 899-905
- DOI: https://doi.org/10.1090/S0002-9939-1989-0976362-9
- PDF | Request permission
Abstract:
A method is given by which pseudocomplemented semilattices can be constructed from graphs. Two consequences of the method are obtained, namely: there exist continuum-many quasivarieties of pseudocomplemented semilattices; for any non-zero cardinal $\kappa$, there exist $\kappa$ pairwise non-isomorphic pseudocomplemented semilattices with isomorphic endomorphism monoids.References
- M. E. Adams, Implicational classes of pseudocomplemented distributive lattices, J. London Math. Soc. (2) 13 (1976), no. 2, 381–384. MR 404075, DOI 10.1112/jlms/s2-13.2.381
- M. E. Adams, V. Koubek, and J. Sichler, Homomorphisms and endomorphisms in varieties of pseudocomplemented distributive lattices (with applications to Heyting algebras), Trans. Amer. Math. Soc. 285 (1984), no. 1, 57–79. MR 748830, DOI 10.1090/S0002-9947-1984-0748830-6
- George Grätzer, General lattice theory, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften, Mathematische Reihe, Band 52, Birkhäuser Verlag, Basel-Stuttgart, 1978. MR 504338
- G. Grätzer and H. Lakser, A note on the implicational class generated by a class of structures, Canad. Math. Bull. 16 (1973), 603–605. MR 369216, DOI 10.4153/CMB-1973-100-4
- G. Grätzer, H. Lakser, and R. W. Quackenbush, On the lattice of quasivarieties of distributive lattices with pseudocomplementation, Acta Sci. Math. (Szeged) 42 (1980), no. 3-4, 257–263. MR 603314
- Z. Hedrlín and J. Sichler, Any boundable binding category contains a proper class of mutually disjoint copies of itself, Algebra Universalis 1 (1971), no. 1, 97–103. MR 285580, DOI 10.1007/BF02944963 G. T. Jones, Pseudocomplemented semilattices, Ph.D. Dissertation, U.C.L.A., 1972.
- Kenneth D. Magill Jr., The semigroup of endomorphisms of a Boolean ring, J. Austral. Math. Soc. 11 (1970), 411–416. MR 0272690
- Carlton J. Maxson, On semigroups of Boolean ring endomorphisms, Semigroup Forum 4 (1972), 78–82. MR 297900, DOI 10.1007/BF02570772
- H. P. Sankappanavar, Remarks on subdirectly irreducible pseudocomplemented semilattices and distributive pseudocomplemented lattices, Math. Japon. 25 (1980), no. 5, 519–521. MR 602279
- B. M. Schein, Ordered sets, semilattices, distributive lattices and Boolean algebras with homomorphic endomorphism semigroups, Fund. Math. 68 (1970), 31–50. MR 272686, DOI 10.4064/fm-68-1-31-50
- Jürg Schmid, Lee classes and sentences for pseudocomplemented semilattices, Algebra Universalis 25 (1988), no. 2, 223–232. MR 950747, DOI 10.1007/BF01229972
- Andrzej Wroński, The number of quasivarieties of distributive lattices with pseudocomplementation, Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. Logic 5 (1976), no. 3, 115–121. MR 460203
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 899-905
- MSC: Primary 06A12; Secondary 08A35, 08C15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0976362-9
- MathSciNet review: 976362