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A free \((-1, 1)\)-algebra with two generators. (Russian) Zbl 0313.17003

A basis of a free \((-1,1)\)-algebra \(A\) has been constructed by two generators and for this algebra \(A\) the following theorem is proved: \(Z(A)=C(A)=D(A)\) , where \(Z(A)\) is the commutative center, \(C(A)\) is the associative-commutative center, \(D(A)\) is an associator ideal of the algebra \(A\). The associative nucleus \(N(A)\) is decomposed into a direct summand of the ideal \(D(A)\) and the square of an ideal generated by commutators.

MSC:

17D20 \((\gamma, \delta)\)-rings, including \((1,-1)\)-rings
17A50 Free nonassociative algebras
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