Browsing Mathematics by Author "Jovanović, Jelena"
Now showing items 11 of 1

Jovanović, Jelena (Beograd , 2016)[more][less]
Abstract: The subject of this dissertation is a syntactic characterization of congruence ^{ semidistributivity in locally nite varieties by Mal'cev conditions (we consider va rieties of idempotent algebras). We prove that no such characterization is possible by a system of identities including one ternary and any number of binary opera tion symbols. The rst characterization is obtained by a strong Mal'cev condition involving two ternary term symbols: A locally nite variety V satis es congruence meet{semidistributivity if and only if there exist ternary terms p and q (inducing idempotent term operations) such that V satis es p(x; x; y) p(x; y; y) p(x; y; x) q(x; y; x) q(x; x; y) q(y; x; x). This condition is optimal in the sense that the number of terms, their arities and the number of identities are the least possible. The second characterization that we nd uses a single 4ary term symbol and is given by the following strong Mal'cev condition t(y; x; x; x) t(x; y; x; x) t(x; x; y; x) t(x; x; x; y) t(y; y; x; x) t(y; x; y; x) t(x; y; y; x) : The third characterization is given by a complete Mal'cev condition: There exist a binary term t(x; y) and wnuterms !n(x1; : : : ; xn) of variety V such that for all n > 3 the following holds: V j= !n(x; x; : : : ; x; y) t(x; y). URI: http://hdl.handle.net/123456789/4450 Files in this item: 1
disertacijaJelenaJovanovic.pdf ( 1.956Mb )
Now showing items 11 of 1