Über die Distributivität des Idealverbandes eines kommutativen Ringes.
It is shown that the implication of an MV-algebra is determined by de Morgan negation operations on a family of quotients of the given algebra; these quotients may be taken to be totally ordered. Certain existing results on the uniqueness of an MV-algebra implication are thereby elucidated and new criteria for uniqueness derived. These rely on a characterisation of chains on which a de Morgan negation is necessarily unique.
We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.
A rotational lattice is a structure where is a lattice and is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices.
The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...
In the paper we deal with weak Boolean products of bounded dually residuated -monoids (DR-monoids). Since bounded DRl-monoids are a generalization of pseudo MV-algebras and pseudo BL-algebras, the results can be immediately applied to these algebras.