Subalgebra lattices of algebras determined by two unary relations and an equivalence relation

Worakrit Supaporn; Passawan Noppakaew; Worakrit Supaporn; Passawan Noppakaew

doi:10.3934/math.2026126

AIMS Mathematics

2026, Volume 11, Issue 2: 3160-3170. doi: 10.3934/math.2026126

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Research article

Subalgebra lattices of algebras determined by two unary relations and an equivalence relation

Worakrit Supaporn ,
Passawan Noppakaew ^,

Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand

Received: 12 November 2025 Revised: 08 January 2026 Accepted: 14 January 2026 Published: 02 February 2026
MSC : 08A30, 08A40, 06B23, 05C60

In this paper, we show the subalgebra lattice of an algebra determined by two nontrivial unary relations and a nontrivial equivalence relation on a finite set. Moreover, we use an algorithm to indicate isomorphic covering graphs of subalgebra lattices. This gives us a lower bound of the number of categorically equivalent classes of clones on a given finite set.
- lattices,
- subalgebras,
- categorical equivalence of clones,
- isomorphic covering graphs
Citation: Worakrit Supaporn, Passawan Noppakaew. Subalgebra lattices of algebras determined by two unary relations and an equivalence relation[J]. AIMS Mathematics, 2026, 11(2): 3160-3170. doi: 10.3934/math.2026126

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Abstract

In this paper, we show the subalgebra lattice of an algebra determined by two nontrivial unary relations and a nontrivial equivalence relation on a finite set. Moreover, we use an algorithm to indicate isomorphic covering graphs of subalgebra lattices. This gives us a lower bound of the number of categorically equivalent classes of clones on a given finite set.

References

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