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Algebraic Properties of Totally Irreducible Elements of Clone Lattices
University of Toronto, Toronto, Canada May 19-May 22
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ISMVL.2004.131992834th International Symposium on Multi ...
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Grant R. Pogosyan, Ivo G. Rosenberg, "Algebraic Properties of Totally Irreducible Elements of Clone Lattices," Multiple-Valued Logic, IEEE International Symposium on, pp. 109-114, 34th International Symposium on Multiple-Valued Logic (ISMVL'04), 2004.
 
 
BibTex
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@article{ 10.1109/ISMVL.2004.1319928,
author = {Grant R. Pogosyan and Ivo G. Rosenberg},
title = {Algebraic Properties of Totally Irreducible Elements of Clone Lattices},
journal ={Multiple-Valued Logic, IEEE International Symposium on},
volume = {0},
year = {2004},
issn = {0195-623X},
pages = {109-114},
doi = {http://doi.ieeecomputersociety.org/10.1109/ISMVL.2004.1319928},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
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TY - CONF
JO - Multiple-Valued Logic, IEEE International Symposium on
TI - Algebraic Properties of Totally Irreducible Elements of Clone Lattices
SN - 0195-623X
SP109
EP114
A1 - Grant R. Pogosyan,
A1 - Ivo G. Rosenberg,
PY - 2004
KW - null
VL - 0
JA - Multiple-Valued Logic, IEEE International Symposium on
ER -
 
Grant R. Pogosyan, International Christian University
Ivo G. Rosenberg, Université deMontréal
Totally join- (meet-) irreducible elements are important for algebraic lattices since the join- (meet-) generates them. We study such elements for clone lattices, particularly for the clone lattice on a k-element universe. We show that in this case the set of totally join- (meet-) irreducible clones is countable; in particular that there are 2^{k - 1} (2^k - 2) countable descending chains of such clones.
Citation:
Grant R. Pogosyan, Ivo G. Rosenberg, "Algebraic Properties of Totally Irreducible Elements of Clone Lattices," ismvl, pp.109-114, 34th International Symposium on Multiple-Valued Logic (ISMVL'04), 2004
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