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Normalizer of a group of “diagonal” automorphisms in algebras over a commutative ring

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Abstract

Let S be a faithful algebra over commutative ring R. It is assumed that S is additively generated by its invertible elements. It is shown that the nomalizer of subgroup Aut(Ss) of group Aut(SR) coincides with the semidirect product Aut(SS) λ Aut(S/R),where the second factor is the group of all ring automorphisms of ring S identical on R.

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Authors
  1. A. H. Al-Hamad
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  2. A. A. Bondarenko
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  3. Z. I. Borevich
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 5–8, 1991.

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Al-Hamad, A.H., Bondarenko, A.A. & Borevich, Z.I. Normalizer of a group of “diagonal” automorphisms in algebras over a commutative ring. J Math Sci 63, 609–611 (1993). https://doi.org/10.1007/BF01097972

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  • DOI: https://doi.org/10.1007/BF01097972

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