## Dually residuated $$\ell$$-monoids having no non-trivial convex subalgebras.(English)Zbl 1125.06012

The paper gives a characterization of simple dually residuated $$\ell$$-monoids (DR$$\ell$$-monoids), i.e. DR$$\ell$$-monoids containing only the trivial convex subalgebra. Based on the known fact that each DR$$\ell$$-monoid is isomorphic to a direct product of an $$\ell$$-group and an lower bounded DR$$\ell$$-monoid, the author proves that a simple DR$$\ell$$-monoid is either an Archimedean totally ordered group or an Archimedean totally ordered generalized pseudo MV-algebra. Consequently, each such DR$$\ell$$-monoid has to be commutative.

### MSC:

 06F05 Ordered semigroups and monoids

Pseudo Hoops
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### References:

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