The normal closure of the coproduct of rings over a division ring

Author:
Wallace S. Martindale

Journal:
Trans. Amer. Math. Soc. **293** (1986), 303-317

MSC:
Primary 16A06; Secondary 16A03, 16A08

MathSciNet review:
814924

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Abstract: Let be the coproduct of -rings and with 1 over a division ring , with at least one of the dimensions , greater than 2. If and are weakly -finite (i.e., one-sided inverses are two-sided) then it is shown that every -inner automorphism of (in the sense of Kharchenko) is inner, unless satisfy one of the following conditions: (I) each is primary (i.e., ), (II) one is primary and the other is -dimensional, (III) char. , one is not a domain, and one is -dimensional. This generalizes a recent joint result with Lichtman (where each was a domain) and an earlier joint result with Montgomery (where each was a domain and was a field).

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DOI:
https://doi.org/10.1090/S0002-9947-1986-0814924-1

Article copyright:
© Copyright 1986
American Mathematical Society