# Weierstrass ring

From Encyclopedia of Mathematics

A local Hensel pseudo-geometric ring (cf. Geometric ring; Hensel ring) each quotient ring of which by a prime ideal is a finite extension of a regular local ring (cf. also 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) over a perfect field, to which the Weierstrass preparation theorem is applicable.

#### References

[1] | M. Nagata, "Local rings" , Interscience (1962) |

[2] | H. Seydi, "Sur la théorie des anneaux de Weierstrass I" Bull. Soc. Math. France , 95 (1971) pp. 227–235 |

**How to Cite This Entry:**

Weierstrass ring.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Weierstrass_ring&oldid=37453

This article was adapted from an original article by V.I. Danilov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article