“Weierstrass ring”的意思、由来-开放百科全书

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Weierstrass ring

释义

Examples
References

In mathematics, a Weierstrass ring, named by {{harvtxt|Nagata|1962|loc=section 45}} after Karl Weierstrass, is a commutative local ring that is Henselian, pseudo-geometric, and such that any quotient ring by a prime ideal is a finite extension of a regular local ring.

Examples

The Weierstrass preparation theorem can be used to show that the ring of convergent power series over the complex numbers in a finite number of variables is a Wierestrass ring. The same is true if the complex numbers are replaced by a perfect field with a valuation.
Every ring that is a finitely-generated module over a Weierstrass ring is also a Weierstrass ring.

References

{{springer|id=W/w097500|first=V. I. |last=Danilov}}
M. Nagata, "Local rings", Interscience (1962)

1 : Commutative algebra

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