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Yet another single law for lattices
Authors:William?McCune  author-information"  >  author-information__contact u-icon-before"  >  mailto:mccune@mcs.anl.gov"   title="  mccune@mcs.anl.gov"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author,R.?Padmanabhan,Robert?Veroff
Affiliation:(1) Mathematics and Computer Science Division, Argonne National Laboratory, 60419 Argonne, Illinois, USA;(2) Department of Mathematics, University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada;(3) Department of Computer Science, University of New Mexico, 87131 Albuquerque, New Mexico, USA
Abstract:In this note we show that the equational theory of all lattices is defined by thesingle absorption law
$$ (((ybigvee x)bigwedge x)bigvee(((zbigwedge(xbigvee
x))bigvee(ubigwedge x))bigwedge v))bigwedge(wbigvee((sbigvee
x)bigwedge(xbigvee t))) = x. $$
This identity of length 29 with 8 variables is shorter than previously known such equationsdefining lattices.
Keywords:Primary: 03G10   Secondary: 06B99.
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