Temat: normal lattice-ordered monoid

Skocz do pozycji: 1.

Tytuł:: On lattice-ordered monoids
Autorzy:: Jasem, Milan
Tematy:: lattice-ordered monoid
normal lattice-ordered monoid
dually residuated lattice-ordered semigroup
direct decomposition
polar; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/728966.pdf Link otwiera się w nowym oknie
Opis:: In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered semigroups are investigated. Normal lattice-ordered monoids are metricless normal lattice-ordered autometrized algebras. It is proved that in any lattice-ordered monoid A, a ∈ A and na ≥ 0 for some positive integer n imply a ≥ 0. A necessary and sufficient condition is found for a lattice-ordered monoid A, such that the set I of all invertible elements of A is a convex subset of A and A¯ ⊆ I, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Direct decompositions of dually residuated lattice-ordered monoids
Autorzy:: Rachůnek, Jiří
Šalounová, Dana
Tematy:: DRl-monoid
lattice-ordered monoid
ideal
normal ideal
polar
direct factor; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/728920.pdf Link otwiera się w nowym oknie
Opis:: 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.
Dostawca treści:: Biblioteka Nauki

Artykuł

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