View source for Weierstrass ring

A local Hensel pseudo-geometric ring (cf. [[Geometric ring|Geometric ring]]; [[Hensel ring|Hensel ring]]) each quotient ring of which by a prime ideal is a finite extension of a regular [[Local ring|local ring]] (cf. also [[Regular ring (in commutative algebra)|Regular ring (in commutative algebra)]]). A Weierstrass ring is analytically irreducible. Any finite extension of a Weierstrass ring is a Weierstrass ring. Examples of Weierstrass rings are analytic rings (rings of convergent power series, cf. [[Analytic ring|Analytic ring]]) over a perfect field, to which the Weierstrass preparation theorem (cf. [[Weierstrass theorem|Weierstrass theorem]]) is applicable.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  M. Nagata,   "Local rings" , Interscience  (1962)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  H. Seydi,   "Sur la théorie des anneaux de Weierstrass I"  ''Bull. Soc. Math. France'' , '''95'''  (1971)  pp. 227–235</TD></TR></table>