Principal tolerances on lattices
Products of locally connected locales
Projectability and weak homogeneity of pseudo effect algebras
In this paper we deal with a pseudo effect algebra possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein, can be represented as an interval of a unital partially ordered group . We prove that is projectable (strongly projectable) if and only if is projectable (strongly projectable). An analogous result concerning weak homogeneity of and of is shown to be valid.
Projective frames : a general view
Properties of complements in the lattice of convergence structures.
Properties of relatively pseudocomplemented directoids
The concept of a relatively pseudocomplemented directoid was introduced recently by the first author. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for...
Pseudo -algebras and -monoids
It is shown that pseudo -algebras are categorically equivalent to certain bounded -monoids. Using this result, we obtain some properties of pseudo -algebras, in particular, we can characterize congruence kernels by means of normal filters. Further, we deal with representable pseudo -algebras and, in conclusion, we prove that they form a variety.
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.
Pseudocomplemented directoids
Directoids as a generalization of semilattices were introduced by J. Ježek and R. Quackenbush in 1990. We modify the concept of a pseudocomplement for commutative directoids and study several basic properties: the Glivenko equivalence, the set of the so-called boolean elements and an axiomatization of these algebras.
Pseudocomplements in sum-ordered partial semirings
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...
Pseudokomplementäre Halbverbände
Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients
The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem...