Abstract
In this survey paper I discuss recent results concerning free algebraic systems and I mention some old results which motivated them. There is no attempt to be comprehensive. The selection of topics is eclectic and personal but with a special emphasis on results of a combinatorial nature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Andréka, B. Jónsson, and I. Németi, Relatively free relation algebras, preprint. K.A.Baker, G.F. McNulty, and W. Taylor [1989], Growth problems for unavoidable words, Theoretical Computer Science, to appear.
R. Balbes and A. Horn [1970], Stone lattices, Duke Math. J. 37, pp. 537–546.
J. Berman and M. Mukaidono [1984], Enumerating fuzzy switching functions and free Kleene algebras, Comp. and Math, with Applications 10, pp. 25–35.
J. Berman and W. Blok [1987], The Fraser-Horn and apple properties, Trans. Amer. Math. Soc. 302, pp. 427–465.
T.C. Brown, [1964], On the finiteness of semigroups in which x r = x, Proc. Cambridge Phil. Soc. 60, pp. 1028–1029.
G. Grätzer [1969], Composition of functions, Proc. Conf. on Universal Algebra, Queen’s Univ. Kingston, Ontario, pp. 1-106.
J.A. Green and D. Rees [1952], On semigroups in which x r = x, Proc. Cambridge Phil. Soc. 48, pp. 35-40.
J. M. Howie [1976], An Introduction to Semigroup Theory, Academic Press.
B. Jonsson and A. Tarski [1956], Two general theorems concerning free algebras, Bull. Amer. Math. Soc. 62, p. 554.
B. Jonsson and A. Tarski [1961], On two properties of free algebras, Math. Scand. 9, pp. 95–101.
J. Kaiman [1958], Lattices with involution, Trans. Amer. Math. Soc. 87, pp. 485–491.
A. Kisielewicz [1981], The p n -sequences of idempotent algebras are strictly increasing, Algebra Universalis 13, pp. 233–250.
A. Kisielewicz [1987], Characterization of p n -sequences for nonidempotent algebras, J. of Alg. 108, pp. 102–115.
A. Kisielewicz, Solution of Marczewski’s problem on algebras with bases of different cardinalities, Fund. Math., to appear.
S. Kleene [1952], Introduction to Metamathematics, pp. 332-340, Van Nostrand.
D. McLean [1954], Idempotent semigroups, Amer. Math. Monthly 61, pp. 110–113.
M. Morse and G. Hedlund [1944], Unending chess, symbolic dynamics, and a problem in semigroups, Duke Math. J. 11, pp. 1–7.
M. Petrich [1973], An Introduction to Semigroups, Charles E. Merril Pub.
J. Plonka [1967], On a method of construction of abstract algebras, Fund. Math. 61, pp. 183–189.
J. Plonka [1969], On equational classes of abstract algebras defined by regular equations, Fund. Math. 64, pp. 241–247.
J. Plonka [1971], On free algebras and algebraic decompositions of algebras from, some equation classes defined by regular equations, Algebra Universalis 1, pp. 261–264.
A.B. Romanowska and J.D.H. Smith [1985], Modal Theory. An Algebraic Approach to Order, Geometry, and Convexity, Helderman Verlag.
M.V. Sapir [1987], Burnside type properties and the finite basis property for varieties of semigroups, Izvestia Akad. Nauk USSR 51, pp. 319–339. (in Russian).
S. Seif [1989], A note on free algebras of discriminator varieties, Algebra Universalis, to appear.
A. Thue, [1912], Ube die gegenseitigen Lage gleicher Teile gewisser Zeichenreihen, Norske Vid. Selsk. Skr. I, Math. Nat. Kl. Christiana I, pp. 1–67.
H. Werner [1978], Discriminator Varieties, Akademie Verlag.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Berman, J. (1990). On the Combinatorics of Free Algebras. In: Almeida, J., Bordalo, G., Dwinger, P. (eds) Lattices, Semigroups, and Universal Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2608-1_2
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2608-1_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-2610-4
Online ISBN: 978-1-4899-2608-1
eBook Packages: Springer Book Archive