Algebraic Properties of Totally Irreducible Elements of Clone Lattices

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34th International Symposium on Multiple-Valued Logic (ISMVL'04)

University of Toronto, Toronto, Canada

May 19-May 22

ISBN: 0-7695-2130-4

	ASCII Text	x
	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	x
	@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	x
	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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ISMVL.2004.1319928

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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