On matrix rapid filters
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 maximal ideals of pseudo-BCK-algebras
We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.
On maximal QROBDD’s of boolean functions
We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).
On maximal QROBDD's of Boolean functions
We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).
On maximal submonoids of BX.
On metric σ-discrete spaces
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 midpoints in lattices
On minimal dynamical systems on Boolean algebras
On minimal ideals in the ring of real-valued continuous functions on a frame
Let be the ring of real-valued continuous functions on a frame . The aim of this paper is to study the relation between minimality of ideals of and the set of all zero sets in determined by elements of . To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame , it is proved that the -ring is isomorphic to the -ring of all real continuous functions on the topological space . Finally, a one-one correspondence is...
On minimal separating Boolean algebras.
On minimal spectrum of multiplication lattice modules
We study the minimal prime elements of multiplication lattice module over a -lattice . Moreover, we topologize the spectrum of minimal prime elements of and study several properties of it. The compactness of is characterized in several ways. Also, we investigate the interplay between the topological properties of and algebraic properties of .
On modular set functions and measures
On modularity in lattices of congruences on ordered sets
On monadic quantale algebras: basic properties and representation theorems
Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.
On Monk’s questions
We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.
On monotone permutations of -cyclically ordered sets
For an -cyclically ordered set with the -cyclic order let be the set of all monotone permutations on . We define a ternary relation on the set . Further, we define in a natural way a group operation (denoted by ) on . We prove that if the -cyclic order is complete and , then is a half cyclically ordered group.
On M-operators of q-lattices
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 multilattices with isomorphic graphs
On Multiset Ordering
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 -fold fuzzy implicative/commutative ideals of BCK-algebras.