Displaying similar documents to “The Lattice of all Systems of r -Ideals in a Set”

On ideals of a skew lattice

João Pita Costa (2012)

Discussiones Mathematicae - General Algebra and Applications

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Ideals are one of the main topics of interest when it comes to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be derived, respectively, from the two concepts of order that arise in the context of skew lattices. The correspondence between the ideals of a skew lattice, derived from the preorder, and the ideals of its respective lattice image is clear....

Some types of implicative ideals

Ladislav Beran (1998)

Commentationes Mathematicae Universitatis Carolinae

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This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.