Weierstrass ring
In mathematics, a Weierstrass ring, named by Nagata (1962, 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.
gollark: Stupid poorly designed command group interface...
gollark: I may have had to execute an emergency shutdown while I make a patch.
gollark: Of course!
gollark: ++magic py await ctx.send("<@263493613860814848> is bees")return None
gollark: ...
References
- Danilov, V. I. (2001) [1994], "Weierstrass ring", Encyclopedia of Mathematics, EMS Press
- M. Nagata, "Local rings", Interscience (1962)
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