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Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Jan Kühr (2008)

Czechoslovak Mathematical Journal

We deal with unbounded dually residuated lattices that generalize pseudo M V -algebras in such a way that every principal order-ideal is a pseudo M V -algebra. We describe the connections of these generalized pseudo M V -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo M V -algebra A by means of the positive cone of a suitable ℓ -group G A . We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex ℓ -subgroups of G A are isomorphic....

Generalized cardinal properties of lattices and lattice ordered groups

Ján Jakubík (2004)

Czechoslovak Mathematical Journal

We denote by K the class of all cardinals; put K ' = K ∪ { ∞ } . Let 𝒞 be a class of algebraic systems. A generalized cardinal property f on 𝒞 is defined to be a rule which assings to each A ∈ 𝒞 an element f A of K ' such that, whenever A 1 , A 2 ∈ 𝒞 and A 1 ≃ A 2 , then f A 1 = f A 2 . In this paper we are interested mainly in the cases when (i) 𝒞 is the class of all bounded lattices B having more than one element, or (ii) 𝒞 is a class of lattice ordered groups.

Generalized F -semigroups

E. Giraldes, P. Marques-Smith, Heinz Mitsch (2005)

Mathematica Bohemica

A semigroup S is called a generalized F -semigroup if there exists a group congruence on S such that the identity class contains a greatest element with respect to the natural partial order ≤ S of S . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup ( S , · , ≤ S ) are determined. It is shown that a semigroup S is a generalized F -semigroup if and only if S contains an anticone, which is a principal order ideal of ( S , ≤ S ) . Also a characterization by means of the structure...

Generating methods for principal topologies on bounded lattices

Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2021)

Kybernetika

In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.

Generators in the category of S-posets

Valdis Laan (2008)

Open Mathematics

The paper contains characterizations of generators and cyclic projective generators in the category of ordered right acts over an ordered monoid.

Graph Monoids.

F.W. Roush, K.H. Kim, L.G. Makar-Limanov (1982)

Semigroup forum

Higher degrees of distributivity in M V -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

In this paper we deal with the of an M V -algebra 𝒜 , where α and β are nonzero cardinals. It is proved that if 𝒜 is singular and ( α , 2 ) -distributive, then it is . We show that if 𝒜 is complete then it can be represented as a direct product of M V -algebras which are homogeneous with respect to higher degrees of distributivity.

Holland’s theorem for pseudo-effect algebras

Anatolij Dvurečenskij (2006)

Czechoslovak Mathematical Journal

We give two variations of the Holland representation theorem for ℓ -groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo M V -algebra can be represented as a pseudo-effect algebra or as a pseudo M V -algebra of automorphisms of some antilattice or of some linearly ordered set.

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