Incomparable Elements in Algebraic Lattices with an Application to AFL-theory

P.R.J. Asveld

Incomparable Elements in Algebraic Lattices with an Application to AFL-theory

P.R.J. Asveld

Research output: Book/Report › Report › Other research output

Abstract

Two special types of algebraic (or compactly generated) lattices, called GG- and GH-lattice, are introduced. These lattices are uncountable, and each element in these lattices (apart from the zero and unit) has an incomparable element. The main results characterize those elements which have a largest incomparable element. Then two particular kinds of algebras, called GG- and GH-algebra, are defined and it is shown that the lattice of subalgebras of a GG-algebra [GH-algebra] is a GG-lattice [GH-lattice]. Finally, some applications to the theory of Abstract Families of Languages (or AFL) are discussed.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente, Department of Applied Mathematics
Number of pages	34
Publication status	Published - 1978

Keywords

HMI-SLT: Speech and Language Technology
EWI-3715

Cite this

Asveld, P. R. J. (1978). Incomparable Elements in Algebraic Lattices with an Application to AFL-theory. Enschede: University of Twente, Department of Applied Mathematics.

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N2 - Two special types of algebraic (or compactly generated) lattices, called GG- and GH-lattice, are introduced. These lattices are uncountable, and each element in these lattices (apart from the zero and unit) has an incomparable element. The main results characterize those elements which have a largest incomparable element. Then two particular kinds of algebras, called GG- and GH-algebra, are defined and it is shown that the lattice of subalgebras of a GG-algebra [GH-algebra] is a GG-lattice [GH-lattice]. Finally, some applications to the theory of Abstract Families of Languages (or AFL) are discussed.

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