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Open Access Research Article

Congruence of order-decreasing and order-preserving on transformations with fixed point

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pp. 2607–2619Vol. 28Issue 7October 2025DOI: 10.47974/JDMSC-1841 Crossmark XML
Received:
11 Jan 2023
Published Online:
24 Apr 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1841
Pages:
2607–2619

Abstract

Let Cn be the semigroup of all order-preserving and order-decreasing transformations on an n-element chain. Let ζ be an idempotent in Cn. The set Cn(ζ) of all α ∈ Cn such that the image of ζ is the set of all fixed points in α is a maximal nilpotent subsemigroup of Cn. For this semigroup, the cardinality and the rank have already determined by Yağci and Kormaz. In the present paper, we characterize all ideals and the maximal as well as minimal congruences on Cn(ζ). Moreover, we consider a class of congruences different from the Rees congruences. 

Keywords

Subject Classifications

20M0520M1720M20

References

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