In mathematics, a Weierstrass ring, named by Nagata 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 Weierstrass 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.
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