Weierstrass Division in Quasianalytic Local Rings
1976 ◽
Vol 28
(5)
◽
pp. 938-953
◽
In this paper we consider the problem of extending the Weierstrass division theorem to quasianalytic local rings of germs of functions of k real variables which properly contain the local ring of germs of analytic functions. After some background material (§ 2) and some technical preliminaries (§ 3), we show by examples that the so-called generic division theorem fails in such rings if k ≧ 1 and that the Weierstrass division theorem fails in such rings if k ≧ 2 (§ 4).
1969 ◽
Vol 21
◽
pp. 106-135
◽
Keyword(s):
1992 ◽
Vol 111
(1)
◽
pp. 47-56
◽
Keyword(s):
2016 ◽
Vol 16
(09)
◽
pp. 1750163
Keyword(s):
2021 ◽
pp. 49-62
Keyword(s):
1980 ◽
Vol 32
(5)
◽
pp. 1261-1265
◽
Keyword(s):
1966 ◽
Vol 27
(1)
◽
pp. 223-230
◽
Keyword(s):
1986 ◽
Vol 38
(1)
◽
pp. 158-178
◽
Keyword(s):
1977 ◽
Vol 68
◽
pp. 123-130
◽