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Automorphisms of the endomorphism semigroup of a free abelian diband. (English) Zbl 1437.08009
By an abelian diband, the author means an algebra $$(A,\circ_1,\circ_2)$$ such that the reducts $$(A,\circ_1)$$ and $$(A,\circ_2)$$ are abelian bands and the identity $$x\circ_1(y\circ_2z) = (x\circ_2y)\circ_1z$$ holds. There are determined all isomorphisms between the endomorphism semigroups of free abelian dibands and it is shown that all authomorphisms of the endomorphism semigroup of a free abelian diband are inner.
##### MSC:
 08B20 Free algebras 17A30 Nonassociative algebras satisfying other identities 08A30 Subalgebras, congruence relations 08A35 Automorphisms and endomorphisms of algebraic structures 20M20 Semigroups of transformations, relations, partitions, etc.