Difference between revisions of "Weierstrass ring"
From Encyclopedia of Mathematics
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| − | A local Hensel pseudo-geometric ring (cf. [[ | + | 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 ring]]s (rings of convergent power series) over a perfect field, to which the [[Weierstrass preparation theorem]] is applicable. |
====References==== | ====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> | + | <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> | ||
Latest revision as of 17:52, 10 January 2016
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://encyclopediaofmath.org/index.php?title=Weierstrass_ring&oldid=37453
Weierstrass ring. Encyclopedia of Mathematics. URL: http://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