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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 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 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 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 ≤ a there exists a direct summand c of a such that b ∧ c is essential in both b and c . Some characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.

Currently displaying 861 – 880 of 3896