SUB-DIRECTLY-IRREDUCIBLES OF CONGRUENCE-DISTRIBUTIVE FINITELY-GENERATED VARIETIES

SUB-DIRECTLY-IRREDUCIBLES OF CONGRUENCE-DISTRIBUTIVE FINITELY-GENERATED VARIETIES | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 12 January 2026 V1 Latest version Share on SUB-DIRECTLY-IRREDUCIBLES OF CONGRUENCE-DISTRIBUTIVE FINITELY-GENERATED VARIETIES Author : Alexej P. Pynko 0000-0002-3478-9850 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176825014.40284280/v1 106 views 84 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Here, we prove that sub-directly-irreducibles of any congruence-distributive variety generated by a finite set of finite algebras are homomorphic images of subalgebras of members of the set, in which case they are finite, their class having a finite skeleton, and so the quasi-variety generated by the set is equational iff every meet-irreducible congruence of each member of the set is the kernel of a homomorphism from the member to a member of the set if each non-one-element subalgebra of every member of the set is simple, these results covering all finitely-generated varieties of lattice expansions. This universal elaboration is applied to the task of characterizing sub-directly-irreducibles of the intrinsic variety of Ha lkowska-Zajac' logic, solution of which results in finding the lattice of its sub-varieties, proper ones forming a four-element diamond. Likewise, as a one more application, we prove that the quasi-variety generated by any expansion of any non-Boolean four-element diamond De Morgan lattice is equational and semi-simple with sub-directly-irreducibles being exactly isomorphic copies of non-one-element subalgebras of the expansion. Supplementary Material File (cd-fin-gen-au.pdf) Download 172.51 KB Information & Authors Information Version history V1 Version 1 12 January 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords congruence-distributive variety de morgan lattice finitely-generated algebra finitely-generated variety lattice simple algebra sub-directly irreducible algebra variety Authors Affiliations Alexej P. Pynko 0000-0002-3478-9850 [email protected] Department of Digital Automata Theory (100), V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine View all articles by this author Metrics & Citations Metrics Article Usage 106 views 84 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Alexej P. Pynko. SUB-DIRECTLY-IRREDUCIBLES OF CONGRUENCE-DISTRIBUTIVE FINITELY-GENERATED VARIETIES. Authorea . 12 January 2026. DOI: https://doi.org/10.22541/au.176825014.40284280/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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