o:14969 Lokalno konačni varijeteti sa polu-distributivnom mrežom kongruencija doktorska disertacija Locally finite varieties with semi{distributive congruence lattice. : doctoral dissertation sr Predmet ove disertacije je sintaksna karakterizacija kongruencijske polu{distributiv- nosti (u odnosu na inmum) lokalno konacnih varijeteta Maljcevljevim uslovima (posmatramo varijetete idempotentnih algebri). Dokazujemo da takva karakteri- zacija nije moguca sistemom identiteta koji koriste jedan ternarni i proizvoljan broj binarnih operacijskih simbola. Prvu karakterizaciju dobijamo jakim Maljcevljevim uslovom koji ukljucuje dva ternarna simbola: Lokalno konacan varijetet V zadovo- ljava uslov kongruencijske polu{distributivnosti (u odnosu na inmum) ako i samo ako postoje ternarni termi p i q (koji indukuju idempotentne term operacije) takvi da V zadovoljava: p(x; x; y) p(x; y; y) p(x; y; x) q(x; y; x) q(x; x; y) q(y; x; x). Ovaj uslov je optimalan u smislu da su broj terma, njihove visestrukosti i broj identiteta najmanji moguci. Druga karakterizacija koju dobijamo koristi jedan 4- arni simbol i data je jakim Maljcevljevim uslovom 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) : Treca karakterizacija je data kompletnim Maljcevljevim uslovom: Postoje binarni term t(x; y) i wnu-termi !n(x1; : : : ; xn) varijeteta V tako za sve n > 3 vazi sledece: V j= !n(x; x; : : : ; x; y) t(x; y). 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 satises congruence meet{semidistributivity if and only if there exist ternary terms p and q (inducing idempotent term operations) such that V satises 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 4-ary 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 wnu-terms !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). Matematika - Algebra / Mathematics - Algebra Datum odbrane: 15.07.2016. lokalno konacan varijetet; mreza kongruencija; polu{distributivnost;wnu{term; Maljcevljev uslov; CSP problem; relaciona sirina; (2; 3){konzistentnost locally nite variety; congruence lattice; meet{semidistributivity; wnu{term; Mal'cev condition; CSP problem; relational width; (2; 3){consistency yes 48818191 91552101 4721 91552100 48818191 2017-04-05T15:03:08.053Z 45 no 46 mentor Jelena. 1975- Jovanović 2016 63 mentor Predrag Tanović 2016 63 član komisije Petar, 1974- Marković 2016 63 član komisije Žarko, 1948- Mijajlović 2016 63 član komisije Nebojša Ikodinović 2016 63 član komisije Predrag Tanović 2016 204 lista 1956478 http://phaidrabg.bg.ac.rs/o:14969 no yes 7 2017-04-05T15:03:08.320Z 70 11 1066609 1066619 1066620 lokalno konacan varijetet; mreza kongruencija; polu{distributivnost;wnu{term; Maljcevljev uslov; CSP problem; relaciona sirina; (2; 3){konzistentnost locally nite variety; congruence lattice; meet{semidistributivity; wnu{term; Mal'cev condition; CSP problem; relational width; (2; 3){consistency 1738 2016