M. E. Adams

Address:

Office: S1 Faculty Office Building
Phone: (845) 257-3572
Fax: (845) 257-3571
E-Mail: adamsm@newpaltz.edu

Research Interests:

• Lattice Theory and Universal Algebra

Recent publications:

• "Q-universal quasivarieties of algebras", Proc. Amer. Math. Soc. 120 (1994), 1053-1059 (with W. Dziobiak).
• "Lattices of quasivarieties of 3-element algebras", J. Algebra 166 (1994), 181-210 (with W. Dziobiak).
• "The Frattini sublattice of a finite distributive lattice", Algebra Universalis 32 (1994), 314-329 (with M. Abad).
• "Equational bases for varieties of Ockham algebras", Algebra Universalis 32 (1994), 368-397 (with H. A. Priestley).
• "Finite semilattices whose non-invertible endomorphisms are products of idempotents", Proc. Roy. Soc. Edinburgh 124 A (1994), 1193-1198 (with S. Bulman-Fleming, M. Gould, and A. Wildsmith).
• "Quasivarieties of distributive lattices with a quantifier", Discrete Math. 135 (1994), 15-28 (with W. Dziobiak).
• "Joins of minimal quasivarieties", Studia Logica 54 (1995), 371-389 (with W. Dziobiak).
• "Quasivarieties of pseudocomplemented semilattices", Fund. Math. 146 (1995), 295-312 (with W. Dziobiak, M. Gould, and J. Schmid).
• "Endomorphism monoids of pseudocomplemented semilattices", Acta Sci. Math. (Szeged) 61 (1995), 3-21 (with M. Gould).
• "Congruence coherent distributive double p-algebras", Proc. Edinburgh Math. Soc 39 (1996), 71-80 (with M. Atallah and R. Beazer).
• "Maximal sublattices of finite distributive lattices", Algebra Universalis 36 (1996), 488-504 (with Ph. Dwinger and J. Schmid).
• "Maximal sublattices and Frattini sublattices of bounded lattices", J. Austral. Math. Soc. (Ser. A) 63 (1997), 110-127 (with R. Freese, J. B. Nation, and J. Schmid).
• "Endomorphism properties of algebraic structures", Proc. Tennessee Topology Conf. (1996), World Scientific Pub. Co., 1997, NJ, 1-17. (with S. Bulman-Fleming and M. Gould).
• "A sufficient condition for Q-universality of a quasivariety and an application", Proc. XVth SIDIM Conf., University of Puerto Rico, Mayaguez, February 25-26th, 2000 (Editors L.Caceres and J.Barety), Antillian College Press, Mayaguez, 9-23 (with W.Dziobiak).
• "Finite posets whose monoids of order-preserving maps are abundant", Acta Sci. Math. (Szeged) 67 (2001), 3-37 (with M. Gould).
• "Finite-to-finite universal quasivarieties are Q-universal", Algebra Universalis 46 (2001), 253-283 (with W. Dziobiak).
• "The lattice of quasivarieties of undirected graphs", Algebra Universalis 47 (2002), 7-11 (with W. Dziobiak).
• "Q-universal varieties of bounded lattices", Algebra Universalis 48 (2002), 333-356 (with W. Dziobiak).
• "Quasivarieties of idempotent semigroups",  Internat. J. Algebra Comput. 13 (2003), 733-752 (with W. Dziobiak).
• "Representable posets and their order components", Cah. Topol. Géom. Différ. Catég. 45 (2004), 179-192 (with D. van der Zypen).
• "Open questions related to the problem of Birkhoff and Maltsev", Studia Logica 78 (2004), 357-378 (with K.V.Adaricheva, W.Dziobiak, and A.V.Kravchenko). (For an up-date on the status of these problems go to http://faculty.ccc.edu/kadaricheva/BirkhoffMalcevProblem.pdf )
• "Countable almost rigid Heyting algebras" , Topics in Discrete Mathematics (Dedicated to Jarik Nesetril on the Occasion of his 60th Birthday), Editors M.Klazar, J.Kratochvil, M.Loebl, J.Matousek, R.Thomas, and P.Valtr, Algorithms and Combinatorics 26, Springer-Verlag, Berlin-Heidelberg, 2006, pp 3-11 (with A.Pultr).
• "The ideal retraction property for idempotent semigroups", Semigroup Forum 74 (2007), 149-154 (with M.Gould).

Forthcoming papers:

• "Endomorphisms of monadic Boolean algebras", Algebra Universalis, to appear (with W.Dziobiak).
• "Endomorphisms of distributive lattices with a quantifier", Internat J. Algebra Comput., to appear (with W.Dziobiak).
• "Pseudocomplemented semilattices are finite-to-finite relatively universal", Algebra Universalis, to appear (with J.Schmid).
• "Minimal extensions of distributive bounded lattices", Houston J. Math., to appear (with J.Schmid).

Published papers related to Priestley Duality:

• "List of published papers", prepared for the special issue of Studia Logica devoted to Priestley Duality (with W.Dziobiak), Volume 56 (1996), 277-290.