A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-18
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
The aim of this paper is to study relations between lattice-valued filters and lattice-valued congruences in residuated lattices.
We introduce a new definition of congruences which just depends on the meet ∧ and the residuum →.
Then it is shown that each of these congruences is automatically a universal-algebra-congruence.
Also, lattice-valued filters and lattice-valued congruences are studied, and it is shown that there is a one-to-one correspondence between the set of all (lattice-valued) filters and the set of all (lattice-valued) congruences.
American Psychological Association (APA)
Wei, Wei& Qiang, Yan& Zhang, Jing. 2013. A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-1032448
Modern Language Association (MLA)
Wei, Wei…[et al.]. A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices. Mathematical Problems in Engineering No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-1032448
American Medical Association (AMA)
Wei, Wei& Qiang, Yan& Zhang, Jing. A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-1032448
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1032448
