Pchelintsev, S. V. A free \((-1, 1)\)-algebra with two generators. (Russian) Zbl 0313.17003 Algebra Logika 13, 425-449 (1974). 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. Reviewer: A. T. Gaĭnov (Novosibirsk) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 10 Documents MSC: 17D20 \((\gamma, \delta)\)-rings, including \((1,-1)\)-rings 17A50 Free nonassociative algebras PDFBibTeX XMLCite \textit{S. V. Pchelintsev}, Algebra Logika 13, 425--449 (1974; Zbl 0313.17003) Full Text: DOI