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Displaying 61 – 80 of 154

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Direct decompositions of dually residuated lattice-ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Discussiones Mathematicae - General Algebra and Applications

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 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 product decompositions of bounded commutative residuated -monoids

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

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

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 ' .

Currently displaying 61 – 80 of 154