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Displaying 861 – 880 of 3879

Direct limits of cyclically ordered groups

Ján Jakubík, Gabriela Pringerová (1994)

Czechoslovak Mathematical Journal

Direct product decomposition of $M V$ -algebras

Ján Jakubík (1994)

Czechoslovak Mathematical Journal

Direct product decomposition of zero-product-associative rings without nilpotent elements

Alexander Abian (1978)

Colloquium Mathematicae

Direct product decompositions of bounded commutative residuated $ℓ$ -monoids

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

The notion of bounded commutative residuated $ℓ$ -monoid ( $B C R$ $ℓ$ -monoid, in short) generalizes both the notions of $M V$ -algebra and of $B L$ -algebra. Let $A ̧$ be a $B C R$ $ℓ$ -monoid; we denote by $ℓ (A ̧)$ the underlying lattice of $A ̧$ . In the present paper we show that each direct...

Direct product decompositions of directed groups

Ján Jakubík (1989)

Czechoslovak Mathematical Journal

Direct product decompositions of infinitely distributive lattices

Ján Jakubík (2000)

Mathematica Bohemica

Let $α$ be an infinite cardinal. Let $𝒯_{α}$ be the class of all lattices which are conditionally $α$ -complete and infinitely distributive. We denote by $𝒯_{σ}^{'}$ the class of all lattices $X$ such that $X$ is infinitely distributive, $σ$ -complete and has the least element. In this paper we deal with direct factors of lattices belonging to $𝒯_{α}$ . As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class $𝒯_{σ}^{'}$ .

Direct product decompositions of pseudo effect algebras

Ján Jakubík (2005)

Mathematica Slovaca

Direct product decompositions of pseudo $M V$ -algebras

Ján Jakubík (2001)

Archivum Mathematicum

In this paper we deal with the relations between the direct product decompositions of a pseudo $M V$ -algebra and the direct product decomposicitons of its underlying lattice.

Direct product factors in GMV-algebras

Jiří Rachůnek, Dana Šalounová (2005)

Mathematica Slovaca

Direct products of weak homomorphisms

Ivan Chajda (1976)

Archivum Mathematicum

Direct summands and retract mappings of generalized $M V$ -algebras

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

In the present paper we deal with generalized $M V$ -algebras ( $G M V$ -algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, $G M V$ -algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of $G M V$ -algebras. The relations between $G M V$ -algebras and lattice ordered groups are essential for this investigation.

Direct summands of Goldie extending elements in modular lattices

Rupal Shroff (2022)

Mathematica Bohemica

In this paper some results on direct summands of Goldie extending elements are studied in a modular lattice. An element $a$ of a lattice $L$ with $0$ is said to be a Goldie extending element if and only if for every $b \leq a$ there exists a direct summand $c$ of $a$ such that $b \land c$ is essential in both $b$ and $c$ . Some characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.

Directed convex subgroups of ordered groups

Jiří Rachůnek (1973)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

Directly decomposable tolerances on direct products of lattices and semilattices

Ivan Chajda, Bohdan Zelinka (1983)

Czechoslovak Mathematical Journal

Directly indecomposable direct factors of a lattice

Ján Jakubík (1996)

Mathematica Bohemica

In this paper we generalize a result of Libkin concerning direct product decompositions of lattices.

Directoid groups

Barry J. Gardner, Michael M. Parmenter (2008)

Czechoslovak Mathematical Journal

We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.

Directoids with an antitone involution

Ivan Chajda, Miroslav Kolařík (2007)

Commentationes Mathematicae Universitatis Carolinae

We investigate $⊓$ -directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation $⊔$ can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids...

Directoids with sectionally antitone involutions and skew MV-algebras

Ivan Chajda, Miroslav Kolařík (2007)

Mathematica Bohemica

It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.

Directoids with sectionally switching involutions

Ivan Chajda (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

It is shown that every directoid equipped with sectionally switching mappings can be represented as a certain implication algebra. Moreover, if the directoid is also commutative, the corresponding implication algebra is defined by four simple identities.

Discrete minimal surface algebras.

Arnlind, Joakim, Hoppe, Jens (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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