scholarly journals Regular local rings essentially of finite type over fields of prime characteristic

2006 ◽  
Vol 306 (2) ◽  
pp. 703-711 ◽  
Author(s):  
Mamoru Furuya ◽  
Hiroshi Niitsuma
Keyword(s):  
Finite Type ◽  
Local Rings ◽  
Prime Characteristic ◽  
Regular Local Rings

Regularity and finite injective dimension in characteristic p > 0

2010 ◽  
Vol 47 (1) ◽  
pp. 108-112
Author(s):  
Tiberiu Dumitrescu ◽  
Cristodor Ionescu
Keyword(s):  
Local Rings ◽  
Prime Characteristic ◽  
Injective Dimension ◽  
Characteristic P ◽  
Frobenius Map ◽  
Regular Local Rings

Recently, the regular local rings of prime characteristic were characterized in terms of the finiteness of injective dimension of the Frobenius map. We obtain relative versions of this result.

scholarly journals A DESCENT THEOREM FOR FORMAL SMOOTHNESS

2016 ◽  
Vol 229 ◽  
pp. 113-140
Author(s):  
JAVIER MAJADAS
Keyword(s):  
Finite Type ◽  
Complete Intersection ◽  
Intersection Property ◽  
Local Rings ◽  
Similar Question ◽  
Regular Local Rings ◽  
Formal Smoothness

We give a descent result for formal smoothness having interesting applications: we deduce that quasiexcellence descends along flat local homomorphisms of finite type, we greatly improve Kunz’s characterization of regular local rings by means of the Frobenius homomorphisms as well as André and Radu relativization of this result, etc. In the second part of the paper, we study a similar question for the complete intersection property instead of formal smoothness, giving also some applications.

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

Factorizations of elements in local rings and semilocal rings of finite type

2019 ◽  
Vol 19 (12) ◽  
pp. 2050234
Author(s):  
María José Arroyo Paniagua ◽  
Alberto Facchini ◽  
Yaser Tolooei
Keyword(s):  
Finite Type ◽  
Local Rings ◽  
Principal Ideals ◽  
Ring Elements

Factorizations of ring elements are described by finite chains of principal ideals. We use the description of cyclically presented modules over local rings to study factorization of elements in local rings.

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