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Classification of L-algebras up to order 4
- Issue Date
- Jun-2024
- Publisher
- University of Hatef
- Keywords
- classification; L-algebra; partial condition; total condition
- Citation
- Journal of Algebraic Hyperstructures and Logical Algebras, v.5, no.1, pp 63 - 86
- Pages
- 24
- Indexed
- SCOPUS
- Journal Title
- Journal of Algebraic Hyperstructures and Logical Algebras
- Volume
- 5
- Number
- 1
- Start Page
- 63
- End Page
- 86
- ISSN
- 2676-6000
2676-6019
- Abstract
- L-algebras, connected to algebraic logic and quantum structures, were first introduced by Rump [13]. In [5], the number of some finite L-algebras is counted. But classi-fying and finding examples of L-algebras is not always an easy task and is very important. So, in this paper, we classify the set of all non-isomorphic L-algebras up to order 4. For this, we define the notion of partial and total conditions and by using them, we characterize all of the L-algebras of orders 2, 3 and 4. We prove that that there are 5 L-algebras of order 3 and 44 L-algebras of order 4, up to isomorphism. © 2024, University of Hatef. All rights reserved.
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Related Researcher
- Ahn, Sun Shin
- College of Education (Department of Mathematics Education)