Weierstrass ring
From HandWiki
In mathematics, a Weierstrass ring, named by Nagata[1] 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
- ↑ (Nagata 1975)
Bibliography
- Hazewinkel, Michiel, ed. (2001), "W/w097500", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=W/w097500
- Nagata, Masayoshi (1975), Local rings, Interscience Tracts in Pure and Applied Mathematics, 13, Interscience Publishers, pp. xiii+234, ISBN 978-0-88275-228-0
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