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A prime ideal and its quotient ring

Published online by Cambridge University Press:  17 April 2009

T. W. Atterton
T. W. Atterton
Affiliation:
University of New South Wales, Kensington, NSW.
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Abstract

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Given arbitrary rings A, B such that A ⊂ B and an arbitrary prime ideal P of A, we show how to construct a quotient ring Ap such that A ⊂ Ap ⊂ B. The ring Ap contains a prime ideal P lying over P and the prime ring A/P may be embedded in Ap/P.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 1 , August 1970 , pp. 107 - 110
Copyright
Copyright © Australian Mathematical Society 1970

References

[1] Atterton, T.W., “Definitions of integral elements and quotient rings over non-commutative rings with identity”, J. Austral. Math. Soc. (to appear).Google Scholar
[2] Jacobson, Nathan, Structure of rings (Colloquium Publ. 37, Amer. Math. Soc., Providence, 1956).CrossRefGoogle Scholar
[3] Utumi, Yuzo, “On quotient rings”, Osaka J. Math. 8 (1956), 1–18.Google Scholar