integral closures
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2020 ◽  
pp. 1
Author(s):  
Goulwen Fichou ◽  
Jean-Philippe Monnier ◽  
Ronan Quarez

2020 ◽  
Vol 27 (02) ◽  
pp. 287-298
Author(s):  
Gyu Whan Chang ◽  
HwanKoo Kim

Let D be an integral domain with quotient field K, [Formula: see text] be the integral closure of D in K, and D[w] be the w-integral closure of D in K; so [Formula: see text], and equality holds when D is Noetherian or dim(D) = 1. The Mori–Nagata theorem states that if D is Noetherian, then [Formula: see text] is a Krull domain; it has also been investigated when [Formula: see text] is a Dedekind domain. We study integral domains D such that D[w] is a Krull domain. We also provide an example of an integral domain D such that [Formula: see text], t-dim(D) = 1, [Formula: see text] is a Prüfer v-multiplication domain with t-dim([Formula: see text]) = 2, and D[w] is a UFD.


2019 ◽  
Vol 372 (9) ◽  
pp. 6655-6676 ◽  
Author(s):  
Michael DiPasquale ◽  
Christopher A. Francisco ◽  
Jeffrey Mermin ◽  
Jay Schweig
Keyword(s):  

2019 ◽  
Vol 19 (03) ◽  
pp. 2050044
Author(s):  
Florian Enescu ◽  
Irina Ilioaea

In this note, we use the theory of test ideals and Cartier algebras to examine the interplay between the tight and integral closures in a local ring of positive characteristic. Using work of Schwede, we prove the abundance of strong test ideals, recovering some older fundamental results, and use this approach in concrete computations. In the second part of the paper, the case of Stanley–Reisner rings is fully examined.


2018 ◽  
Vol 222 (11) ◽  
pp. 3560-3565 ◽  
Author(s):  
Anuj Jakhar ◽  
Sudesh K. Khanduja ◽  
Neeraj Sangwan

2018 ◽  
Vol 87 ◽  
pp. 140-175 ◽  
Author(s):  
Hayden D. Stainsby
Keyword(s):  

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