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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.
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