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The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.

Direct factors of directed groups

Judita Lihová (1991)

Archivum Mathematicum

Direct factors of multilattice groups

Milan Kolibiar (1990)

Archivum Mathematicum

Direct factors of multilattice groups. II.

Milan Kolibiar (1992)

Archivum Mathematicum

Subgroups of a directed distributive multilattice group $G$ are characterized which are direct factors of $G$ . The main result is formulated in Theorem 2.

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

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