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All ordered sets having amenable lattice orders

In: Mathematica Slovaca, vol. 52, no. 1
Chawewan Ratanaprasert
Detaily:
Rok, strany: 2002, 1 - 11
O článku:
Kolibiar, Rosenberg and Schweigert proved that all compatible orders $≤$ on the set $P$ of a lattice $L = (P; ≤*)$ stem from $2$@-factor subdirect representations of $L$. We denote this by $P \# L$ and call $≤*$ amenable lattice order of an ordered set $P = (P; ≤)$. In this paper, we first give necessary and sufficient conditions for an order to be compatible with a lattice. We show that an ordered set has an amenable lattice order just if each its order component has. Further, we prove that there is a bijection between the connected compatible orders of a lattice and the pairs of complementary congruence relations on the lattice. Finally, we characterize all ordered sets having an amenable lattice order.
Ako citovať:
ISO 690:
Ratanaprasert, C. 2002. All ordered sets having amenable lattice orders. In Mathematica Slovaca, vol. 52, no.1, pp. 1-11. 0139-9918.

APA:
Ratanaprasert, C. (2002). All ordered sets having amenable lattice orders. Mathematica Slovaca, 52(1), 1-11. 0139-9918.