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On varieties of graphs

Alfonz Haviar, Roman Nedela (1998)

Discussiones Mathematicae Graph Theory

In this paper, we introduce the notion of a variety of graphs closed under isomorphic images, subgraph identifications and induced subgraphs (induced connected subgraphs) firstly and next closed under isomorphic images, subgraph identifications, circuits and cliques. The structure of the corresponding lattices is investigated.

On varieties of left distributive left idempotent groupoids

David Stanovský (2004)

Discussiones Mathematicae - General Algebra and Applications

We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xⁿ ≈ x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.

On varieties of orgraphs

Alfonz Haviar, Gabriela Monoszová (2001)

Discussiones Mathematicae Graph Theory

In this paper we investigate varieties of orgraphs (that is, oriented graphs) as classes of orgraphs closed under isomorphic images, suborgraph identifications and induced suborgraphs, and we study the lattice of varieties of tournament-free orgraphs.

On varieties of pseudo M V -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

In this paper we investigate the relation between the lattice of varieties of pseudo M V -algebras and the lattice of varieties of lattice ordered groups.

Orthocomplemented difference lattices with few generators

Milan Matoušek, Pavel Pták (2011)

Kybernetika

The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result...

Orthorings

Ivan Chajda, Helmut Länger (2004)

Discussiones Mathematicae - General Algebra and Applications

Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.

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