scholarly journals Non-commutative regular local rings of dimension 2

1988 ◽  
Vol 115 (1) ◽  
pp. 219-237 ◽  
Author(s):  
A.W Chatters
Keyword(s):  
Local Rings ◽  
Dimension 2 ◽  
Regular Local Rings

scholarly journals Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings

2001 ◽  
Vol 162 ◽  
pp. 87-110 ◽  
Author(s):  
Kei-Ichi Watanabe ◽  
Ken-Ichi Yoshida
Keyword(s):  
Local Rings ◽  
Two Dimensional ◽  
Dimension 2 ◽  
Regular Local Rings

We study the behavior of Hilbert-Kunz multiplicity for powers of an ideal, especially the case of stable ideals and ideals in local rings of dimension 2. We can characterize regular local rings by certain equality between Hilbert-Kunz multiplicity and usual multiplicity.We show that rings with “minimal” Hilbert-Kunz multiplicity relative to usual multiplicity are “Veronese subrings” in dimension 2.

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
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