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Freely adjoining a complement to a lattice

In: Mathematica Slovaca, vol. 56, no. 1
G. Grätzer - H. Lakser

Details:

Year, pages: 2006, 93 - 104
About article:
For a bounded lattice $K$ and an element $a$ of $K - \{0,1\}$, we directly describe the structure of the lattice freely generated by $K$ and an element $u$ subject to the requirement that $u$ be a complement of $a$. Earlier descriptions of this lattice used multi-step procedures. As an application, we give a short and direct proof of the classical result of R. P. Dilworth (1945): Every lattice can be embedded into a uniquely complemented lattice. We prove it in the stronger form due to C. C. Chen and G. Grätzer (1969): {\it Every at most uniquely complemented bounded lattice has a $\{0,1\}$@-embedding into a uniquely complemented lattice}.
How to cite:
ISO 690:
Grätzer, G., Lakser, H. 2006. Freely adjoining a complement to a lattice. In Mathematica Slovaca, vol. 56, no.1, pp. 93-104. 0139-9918.

APA:
Grätzer, G., Lakser, H. (2006). Freely adjoining a complement to a lattice. Mathematica Slovaca, 56(1), 93-104. 0139-9918.