On the primitivity of polynomial rings with nonprimitive coefficient rings

Author:
T. J. Hodges

Journal:
Proc. Amer. Math. Soc. **98** (1986), 553-558

MSC:
Primary 16A20

MathSciNet review:
861748

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Abstract: For a hereditary noetherian prime ring with classical quotient ring , various necessary and sufficient conditions are given for the polynomial ring to be primitive when itself is not primitive. It is shown that if is a local hereditary noetherian prime ring, then is primitive if and only if is primitive. Similarly, for a semilocal hereditary noetherian prime ring whose Jacobson radical contains a nonzero central element, it is shown that is primitive if and only if is primitive.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0861748-0

Keywords:
Primitivity,
polynomial rings,
hereditary noetherian prime rings

Article copyright:
© Copyright 1986
American Mathematical Society