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Modal operators on bounded commutative residuated $$\ell$$-monoids. (English) Zbl 1150.06016
Bounded commutative R$$\ell$$-monoids are bounded integral commutative residuated lattices satisfying the divisibility identity $$x\odot (x\rightarrow y)=x\wedge y$$. The present paper generalizes results of {D. S. Macnab} [Algebra Univers. 12, 5–29 (1981; Zbl 0459.06005)]. A modal operator on an R$$\ell$$-monoid $$M$$ is defined as a mapping $$f\colon M\to M$$ such that (i) $$x\leq f(x)$$, (ii) $$f(f(x))=f(x)$$, (iii) $$f(x\odot y)=f(x)\odot f(y)$$, and various properties of such mappings are studied.

##### MSC:
 06F05 Ordered semigroups and monoids 06D35 MV-algebras
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##### References:
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