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On the endomorphism monoids of (uniquely) complemented lattices |
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| Authors: | G. Grä tzer J. Sichler |
| Affiliation: | Department of Mathematics, University of Manitoba, Winnipeg MB R3T 2N2, Canada ; Department of Mathematics, University of Manitoba, Winnipeg MB R3T 2N2, Canada |
| Abstract: | Let |
| Keywords: | Endomorphism monoid complemented lattice uniquely complemented lattice |
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be a lattice with 
and 
. An endomorphism 
of 
is a 
-endomorphism, if it satisfies 
and 
. The 
-endomorphisms of 
form a monoid. In 1970, the authors proved that every monoid 
can be represented as the 
-endomorphism monoid of a suitable lattice 
with 
and 
. In this paper, we prove the stronger result that the lattice 
with a given 
-endomorphism monoid 
can be constructed as a uniquely complemented lattice; moreover, if 
is finite, then 
can be chosen as a finite complemented lattice.