<p>Ako je Lalgebarska mreža i a kodistributivan elemenat u L, onda sve klase kongruencije (pa indukovane homomorfizmom ma : xi— > a A x imaju najveće elemente. Najveći elemenat klase kojoj x E Lpripada je označen sa x.Ako je *a binarna op­eracija definisana sa x *ay = (x A y) V (x A y),onda je istraživana struktura (L, *a), i odgovarajući poset ( L, <»). Kao primer takve strukture posmatrana je algebra slabih kongruencija (CwA, *a), gde je *a specijalna grafička kompozicija. Dobijeni rezultati daju prirodne posledice u strukturi slabih kongruencija. Data je primena ovih rezultata u univerzalnoj algebri. Njihovom primenom karakterizuje se CEP i Hamiltonovo svojstvo. Dat je potreban i dovoljan uslov da poset (L, < -) bude mreža i ovi rezultati su primenjeni na mrežu slabih kongruencija.</p> / <p>If Lis an algebraic lattice and a codistributive element in L,then all the classes of the congruences 4>a determined by the homomorphism ma : x \— > a Ax have top elements. The top element of the class which to belongs an x € Lis denoted by x. If *a is a binary operation defined by x *ay= (xA y) V (xA y),then we investigate the<br />structure (L,*a), and the corresponding poset (L, < t ). Asan example of such a structure we observe an algebra of weak congruences ( C w A , * a),where *a is a special graphical composition. We obtain natural conse­ quences of the mentioned results to the structure weak congruences. An application in universal algebra is presented, for example, we characterized CEP and Hamiltonian property. Necessary and sufficient conditions for a poset (L,<*) to be a lattice are given, and the results are applied in the case of weak congruence lattices.</p>
Identifer | oai:union.ndltd.org:uns.ac.rs/oai:CRISUNS:(BISIS)73361 |
Date | 13 July 2001 |
Creators | Lazarević Vera |
Contributors | Tepavčević Andreja, Janez Ušan, Žižović Mališa, Šešelja Branimir |
Publisher | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, University of Novi Sad, Faculty of Sciences at Novi Sad |
Source Sets | University of Novi Sad |
Language | Serbian |
Detected Language | English |
Type | PhD thesis |
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