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On interval decomposition lattices

Stephan Foldes, Sándor Radeleczki (2004)

Discussiones Mathematicae - General Algebra and Applications

Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.

On JP-semilattices of Begum and Noor

Jānis Cīrulis (2013)

Mathematica Bohemica

In recent papers, S. N. Begum and A. S. A. Noor have studied join partial semilattices (JP-semilattices) defined as meet semilattices with an additional partial operation (join) satisfying certain axioms. We show why their axiom system is too weak to be a satisfactory basis for the authors' constructions and proofs, and suggest an additional axiom for these algebras. We also briefly compare axioms of JP-semilattices with those of nearlattices, another kind of meet semilattices with a partial join...

On k-radicals of Green's relations in semirings with a semilattice additive reduct

Tapas Kumar Mondal, Anjan Kumar Bhuniya (2013)

Discussiones Mathematicae - General Algebra and Applications

We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.

On matrix rapid filters

Winfried Just, Peter Vojtáš (1997)

Fundamenta Mathematicae

Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.

On metric σ-discrete spaces

Szymon Plewik, Marta Walczyńska (2016)

Banach Center Publications

By studying dimensional types of metric scattered spaces, we consider the wider class of metric σ-discrete spaces. Applying techniques relevant to this wider class, we present new proofs of some embeddable properties of countable metric spaces in such a way that they can be generalized onto uncountable metric scattered spaces. Related topics are also explored, which gives a few new results.

On M-operators of q-lattices

Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.

On Multiset Ordering

Grzegorz Bancerek (2016)

Formalized Mathematics

Formalization of a part of [11]. Unfortunately, not all is possible to be formalized. Namely, in the paper there is a mistake in the proof of Lemma 3. It states that there exists x ∈ M1 such that M1(x) > N1(x) and (∀y ∈ N1)x ⊀ y. It should be M1(x) ⩾ N1(x). Nevertheless we do not know whether x ∈ N1 or not and cannot prove the contradiction. In the article we referred to [8], [9] and [10].

On n-normal posets

Radomír Halaš, Vinayak Joshi, Vilas Kharat (2010)

Open Mathematics

A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained.

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