Posets having a selfdual interval poset
Posets having a unique decomposition into the minimum number of antichains. (Short Communication).
Posets having a unique decomposition into the minimum number of antichains.
Power-ordered sets
We define a natural ordering on the power set 𝔓(Q) of any finite partial order Q, and we characterize those partial orders Q for which 𝔓(Q) is a distributive lattice under that ordering.
Powers of partially ordered sets: Cancellation and reffinement properties.
Powers of partially ordered sets: The automorphism group.
Prime and maximal ideals of partially ordered sets
Prime elements in the semigroup of finite types of partially ordered sets in cardinal multiplication
Prime ideals in 0-distributive posets
In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in which atoms are dually distributive. Further, it is proved that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime. The second section focuses on the characterizations of (minimal) prime ideals in pseudocomplemented posets. The third section deals with the generalization...
Primeness and semiprimeness in posets
The concept of a semiprime ideal in a poset is introduced. Characterizations of semiprime ideals in a poset as well as characterizations of a semiprime ideal to be prime in are obtained in terms of meet-irreducible elements of the lattice of ideals of and in terms of maximality of ideals. Also, prime ideals in a poset are characterized.
Profile classes and partial well-order for permutations.
Properties of monotone mappings in partially ordered sets.
Pseudocomplemented and Stone Posets
We show that every pseudocomplemented poset can be equivalently expressed as a certain algebra where the operation of pseudocomplementation can be characterized by means of remaining two operations which are binary and nullary. Similar characterization is presented for Stone posets.
Pseudodimension of relational structures
Quantized dual graded graphs.
Quasi-hereditary algebras which are twisted double incidence algebras of posets.
Quasi-minimal posets and lattices.
Quasiorder on Systems of Directed Sets
Quasi-orders of algebras
Quasi-regular Relations – A New Class of Relations on Sets