Reference : Associative idempotent nondecreasing functions are reducible
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Physical, chemical, mathematical & earth Sciences : Mathematics
Associative idempotent nondecreasing functions are reducible
Kiss, Gergely mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Somlai, Gabor [Eotvos Lorand University Budapest > Algebra]
[en] n-ary semigroup ; associativity ; reducible ; idempotent ; quasitrivial ; extremal
[en] An n-variable associative function is called reducible if it can be
written as a composition of a binary associative function. In this paper we
summarize the known results when the function is defined on a chain and nondecreasing.
The main result of this paper shows that associative idempotent
and nondecreasing functions are uniquely reducible.

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