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Free rectangular dibands and free dimonoids. (English) Zbl 1279.08008
Summary: We construct a free rectangular diband and describe its structure. We also present the least rectangular diband congruence, the least $$(rb,rz)$$-congruence, the least left zero and right zero congruence, the least rectangular band congruence and the least left zero congruence on free dimonoids and use them to obtain decompositions of free dimonoids.

##### MSC:
 08B20 Free algebras 08A30 Subalgebras, congruence relations 20M99 Semigroups
##### Keywords:
rectangular dimonoid; free dimonoid; diband of subdimonoids