ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXII, 2 (2003)
p. 147 – 157
On Subgroupoid Lattices of some Finite Groupoid
K. Pioro
Abstract.
We investigate finite commutative groupoids $\mathcal{G}=\langle
G,\circ\rangle$ such that
$g\circ h\neq g$ for all elements $g,h$
of $\mathcal{G}$. First, we show that for any such groupoid, its
weak (i.e. partial) subgroupoid lattice uniquely determines its
subgroupoid lattice. Next, we characterize the lattice of all weak
subgroupoids of such a groupoid. This is a distributive finite
lattice satisfying some combinatorial conditions concerning its
atoms and join--irreducible elements.
AMS subject classification:
05C65, 05C99, 08A30, 08A55, 20N02, Secondary::05C90, 06B05, 08A05, 08A62
Keywords:
Finite groupoid, partial groupoid, partial and total subgroupoids, subgroupoid lattices, hypergraph,
functional directed graph
Download: Adobe PDF 
Compressed Postscript 
Version to read: Adobe PDF
Acta Mathematica Universitatis Comenianae
Institute of Applied Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic
Telephone: + 421-2-60295111 Fax: + 421-2-65425882
e-Mail: amuc@fmph.uniba.sk
Internet: www.iam.fmph.uniba.sk/amuc
©
Copyright 2003, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE