Algebarske strukture oslabljenih mreža i primene
Algebraic structures of weakened lattices and applications
Author
Lazarević, VeraMentor
Tepavčević, AndrejaCommittee members
Janez, UšanTepavčević, Andreja
Žižović, Mališa
Šešelja, Branimir
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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.
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 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.