Approximating discrete valuation rings by regular local rings

2021 ◽  
pp. 165-172
Keyword(s):  
Local Rings ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Regular Local Rings

scholarly journals Approximating discrete valuation rings by regular local rings

2000 ◽  
Vol 129 (1) ◽  
pp. 37-43
Author(s):  
William Heinzer ◽  
Christel Rotthaus ◽  
Sylvia Wiegand
Keyword(s):  
Local Rings ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Regular 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

scholarly journals On cuspidal representations of general linear groups over discrete valuation rings

2010 ◽  
Vol 175 (1) ◽  
pp. 391-420 ◽  
Author(s):  
Anne-Marie Aubert ◽  
Uri Onn ◽  
Amritanshu Prasad ◽  
Alexander Stasinski
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Cuspidal Representations

Right Invariant Right Hereditary Rings

1974 ◽  
Vol 26 (5) ◽  
pp. 1186-1191 ◽  
Author(s):  
H. H. Brungs
Keyword(s):  
Principal Ideal ◽  
Prime Ideals ◽  
Maximal Orders ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
Dedekind Domains ◽  
Left Order ◽  
Principal Ideal Domains

Let R be a right hereditary domain in which all right ideals are two-sided (i.e., R is right invariant). We show that R is the intersection of generalized discrete valuation rings and that every right ideal is the product of prime ideals. This class of rings seems comparable with (and contains) the class of commutative Dedekind domains, but the rings considered here are in general not maximal orders and not Dedekind rings in the terminology of Robson [9]. The left order of a right ideal of such a ring is a ring of the same kind and the class contains right principal ideal domains in which the maximal right ideals are two-sided [6].

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