scholarly journals Link between Noetherianity and the Weierstrass Division Theorem on some quasianalytic local rings

2012 ◽  
Vol 140 (11) ◽  
pp. 3883-3892 ◽  
Author(s):  
Abdelhafed Elkhadiri
Keyword(s):  
Local Rings ◽  
Division Theorem

Weierstrass Division in Quasianalytic Local Rings

1976 ◽  
Vol 28 (5) ◽  
pp. 938-953 ◽  
Author(s):  
C. L. Childress
Keyword(s):  
Local Ring ◽  
Analytic Functions ◽  
Local Rings ◽  
Division Theorem ◽  
Background Material

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).

scholarly journals Some properties of the polynomially bounded o-minimal expansions of the real field and of some quasianalytic local rings

2020 ◽  
Vol 12 (2) ◽  
pp. 483-491
Author(s):  
M. Berraho
Keyword(s):  
Metric Spaces ◽  
Real Field ◽  
Local Rings ◽  
Topological Properties ◽  
The Real ◽  
Division Theorem

In this paper, we study the Weierstrass division theorem over the rings of smooth germs that are definable in an arbitrary polynomially bounded o-minimal expansion of the real field by giving some criteria for satisfying this theorem. Afterwards, we study some topological properties of some quasianalytic subrings of the ring of smooth germs for the $(x_1)$-adic topology by showing that these rings are separable metric spaces. Also, we cite a criterion for their completeness with respect to the $(x_1)$-adic topology.

scholarly journals Weierstrass division theorem in quasianalytic local rings

2008 ◽  
Vol 185 (1) ◽  
pp. 83-86 ◽  
Author(s):  
Abdelhafed Elkhadiri ◽  
Hassan Sfouli
Keyword(s):  
Local Rings ◽  
Division Theorem

scholarly journals Correction to: Classification of non-local rings with genus two zero-divisor graphs

2021 ◽  
Vol 25 (4) ◽  
pp. 3355-3356
Author(s):  
T. Asir ◽  
K. Mano ◽  
T. Tamizh Chelvam
Keyword(s):  
Zero Divisor ◽  
Local Rings ◽  
Non Local ◽  
Genus Two

scholarly journals Analytic ramifications and flat couples of local rings

1981 ◽  
Vol 146 (0) ◽  
pp. 201-208 ◽  
Author(s):  
Tomas Larfeldt ◽  
Christer Lech
Keyword(s):  
Local Rings

scholarly journals Characterizations of regular local rings via syzygy modules of the residue field

2018 ◽  
Vol 10 (3) ◽  
pp. 327-337
Author(s):  
Dipankar Ghosh ◽  
Anjan Gupta ◽  
Tony J. Puthenpurakal
Keyword(s):  
Residue Field ◽  
Local Rings ◽  
Syzygy Modules ◽  
Regular Local Rings

The isomorphisms of orthogonal groups over local rings

1986 ◽  
Vol 2 (4) ◽  
pp. 281-291
Author(s):  
Tang Xiangpu ◽  
An Jianbei
Keyword(s):  
Local Rings ◽  
Orthogonal Groups
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