Page 1 Next

Displaying 1 – 20 of 21

Showing per page

On a theorem of Cantor-Bernstein type for algebras

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

Freytes proved a theorem of Cantor-Bernstein type for algbras; he applied certain sequences of central elements of bounded lattices. The aim of the present paper is to extend the mentioned result to the case when the lattices under consideration need not be bounded; instead of sequences of central elements we deal with sequences of internal direct factors of lattices.

On algebra-lattices

Jiří Rachůnek (1984)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On Butler B ( 2 ) -groups decomposing over two base elements

Clorinda de Vivo, Claudia Metelli (2009)

Commentationes Mathematicae Universitatis Carolinae

A B ( 2 ) -group is a sum of a finite number of torsionfree Abelian groups of rank 1 , subject to two independent linear relations. We complete here the study of direct decompositions over two base elements, determining the cases where the relations play an essential role.

On central atoms of Archimedean atomic lattice effect algebras

Martin Kalina (2010)

Kybernetika

If element z of a lattice effect algebra ( E , , 0 , 1 ) is central, then the interval [ 0 , z ] is a lattice effect algebra with the new top element z and with inherited partial binary operation . It is a known fact that if the set C ( E ) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C ( E ) in E equals to the top element of E , then E is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether C ( E ) is a bifull sublattice...

On generalized topological spaces I

Artur Piękosz (2013)

Annales Polonici Mathematici

We begin a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings. We reformulate the axioms. Generalized topology is found to be connected with the concept of a bornological universe. Both GTS and its full subcategory SS of small spaces are topological categories. The second part of this paper will also appear in this journal.

On generalized topological spaces II

Artur Piękosz (2013)

Annales Polonici Mathematici

This is the second part of A. Piękosz [Ann. Polon. Math. 107 (2013), 217-241]. The categories GTS(M), with M a non-empty set, are shown to be topological. Several related categories are proved to be finitely complete. Locally small and nice weakly small spaces can be described using certain sublattices of power sets. Some important elements of the theory of locally definable and weakly definable spaces are reconstructed in a wide context of structures with topologies.

On ideal theory of hoops

Mona Aaly Kologani, Rajab Ali Borzooei (2020)

Mathematica Bohemica

In this paper, we define and characterize the notions of (implicative, maximal, prime) ideals in hoops. Then we investigate the relation between them and prove that every maximal implicative ideal of a -hoop with double negation property is a prime one. Also, we define a congruence relation on hoops by ideals and study the quotient that is made by it. This notion helps us to show that an ideal is maximal if and only if the quotient hoop is a simple MV-algebra. Also, we investigate the relationship...

On M-operators of q-lattices

Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.

On reflexive closed set lattices

Zhongqiang Yang, Dong Sheng Zhao (2010)

Commentationes Mathematicae Universitatis Carolinae

For a topological space X , let S ( X ) denote the set of all closed subsets in X , and let C ( X ) denote the set of all continuous maps f : X X . A family 𝒜 S ( X ) is called reflexive if there exists 𝒞 C ( X ) such that 𝒜 = { A S ( X ) : f ( A ) A for every f 𝒞 } . Every reflexive family of closed sets in space X forms a sub complete lattice of the lattice of all closed sets in X . In this paper, we continue to study the reflexive families of closed sets in various types of topological spaces. More necessary and sufficient conditions for certain families of closed...

Currently displaying 1 – 20 of 21

Page 1 Next