Direct decompositions of dually residuated lattice-ordered monoids
Jiří Rachůnek, Dana Šalounová · Discussiones Mathematicae - General Algebra and Applications · 2004
The class of dually residuated lattice ordered monoids (DRℓ-monoids) contains, in an appropriate signature, all ℓ-groups, Brouwerian algebras, M V -and GM V -algebras, BL-and pseudo BL-algebras, etc.In the paper we study direct products and decompositions of DRℓmonoids 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.