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On join-complete implication algebras.
- Source :
-
Soft Computing - A Fusion of Foundations, Methodologies & Applications . Jul2024, Vol. 28 Issue 13/14, p7701-7708. 8p. - Publication Year :
- 2024
-
Abstract
- In this paper, first, we consider an algebra that has a binary operation and a join of arbitrary nonempty subset. A lattice implication algebra is a lattice with a binary operation, which has a join and a meet of finite nonempty subsets. In this work, the notion of join-complete implication algebras L is defined as a join-complete lattice with a binary operation, and some properties of this algebra L are searched. Moreover, we prove that the interval [a, 1] in L is a lattice implication algebra and show that L satisfies the completely distributive law when it has the smallest element 0. Finally, we state the concept of filter and multipliers of L and provide finite and infinite examples of them. In addition, we research some properties of these concepts in detail. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*BINARY operations
Subjects
Details
- Language :
- English
- ISSN :
- 14327643
- Volume :
- 28
- Issue :
- 13/14
- Database :
- Academic Search Index
- Journal :
- Soft Computing - A Fusion of Foundations, Methodologies & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 179087598
- Full Text :
- https://doi.org/10.1007/s00500-023-09624-5