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On the embedding of ordered semigroups into ordered group

Mohammed Ali Faya Ibrahim (2004)

Czechoslovak Mathematical Journal

It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L -maher and R -maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R -maher semigroup can be embedded into an ordered group.

On the existence of prime ideals in Boolean algebras

Jörg Flum (1999)

Banach Center Publications

Rasiowa and Sikorski [5] showed that in any Boolean algebra there is an ultrafilter preserving countably many given infima. In [3] we proved an extension of this fact and gave some applications. Here, besides further remarks, we present some of these results in a more general setting.

On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth

Stanisław Kasjan, Grzegorz Pastuszak (2014)

Colloquium Mathematicae

Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.

On the extension of D -poset valued measures

Beloslav Riečan (1998)

Czechoslovak Mathematical Journal

A variant of Alexandrov theorem is proved stating that a compact, subadditive D -poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.

On the height of order ideals

Gábor Czédli, Miklós Maróti (2010)

Mathematica Bohemica

We maximize the total height of order ideals in direct products of finitely many finite chains. We also consider several order ideals simultaneously. As a corollary, a shifting property of some integer sequences, including digit sum sequences, is derived.

On the injectivity of Boolean algebras

Bernhard Banaschewski (1993)

Commentationes Mathematicae Universitatis Carolinae

The functor taking global elements of Boolean algebras in the topos 𝐒𝐡 𝔅 of sheaves on a complete Boolean algebra 𝔅 is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in 𝔅 -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.

On the jump number of lexicographic sums of ordered sets

Hyung Chan Jung, Jeh Gwon Lee (2003)

Czechoslovak Mathematical Journal

Let Q be the lexicographic sum of finite ordered sets Q x over a finite ordered set P . For some P we can give a formula for the jump number of Q in terms of the jump numbers of Q x and P , that is, s ( Q ) = s ( P ) + ∑ x ∈ P s ( Q x ) , where s ( X ) denotes the jump number of an ordered set X . We first show that w ( P ) - 1 + ∑ x ∈ P s ( Q x ) ≤ s ( Q ) ≤ s ( P ) + ∑ x ∈ P s ( Q x ) , where w ( X ) denotes the width of an ordered set X . Consequently, if P is a Dilworth ordered set, that is, s ( P ) = w ( P ) - 1 , then the formula holds. We also show that it holds again if P is bipartite. Finally, we prove that the lexicographic sum of...

On the L -valued categories of L - E -ordered sets

Olga Grigorenko (2012)

Kybernetika

The aim of this paper is to construct an L -valued category whose objects are L - E -ordered sets. To reach the goal, first, we construct a category whose objects are L - E -ordered sets and morphisms are order-preserving mappings (in a fuzzy sense). For the morphisms of the category we define the degree to which each morphism is an order-preserving mapping and as a result we obtain an L -valued category. Further we investigate the properties of this category, namely, we observe some special objects, special...

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