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A Theorem On Zariski Rings

Published online by Cambridge University Press:  20 November 2018

Michio Yoshida
Michio Yoshida*
Affiliation:
Hiroshima University
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Given a Noetherian ring A with unit element and an ideal m of A such that

,

we may topologize A by adopting {mn; n = 1, 2, …} as a fundamental system of neighborhoods of 0. This topologized ring is usually referred to as an m-adic ring, and is called a Zariski ring if its ideals are all closed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 3 - 4
Copyright
Copyright © Canadian Mathematical Society 1956

References

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