Displaying similar documents to “On modules in which idempotent reducts form a chain”

The structure of idempotent residuated chains

Wei Chen, Xian Zhong Zhao (2009)

Czechoslovak Mathematical Journal

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In this paper we study some special residuated lattices, namely, idempotent residuated chains. After giving some properties of Green’s relation 𝒟 on the monoid reduct of an idempotent residuated chain, we establish a structure theorem for idempotent residuated chains. As an application, we give necessary and sufficient conditions for a band with an identity to be the monoid reduct of some idempotent residuated chain. Finally, based on the structure theorem for idempotent residuated chains,...

Idempotent operators on a finite chain.

Margalida Mas Grimalt, Joan Torrens, Tomasa Calvo, Marc Carbonell (1999)

Mathware and Soft Computing

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This work is devoted to find and study some possible idempotent operators on a finite chain L. Specially, all idempotent operators on L which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum.