krull domains
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Author(s):  
Gyu Whan Chang

AbstractLet D be an integrally closed domain, $$\{V_{\alpha }\}$$ { V α } be the set of t-linked valuation overrings of D, and $$v_c$$ v c be the star operation on D defined by $$I^{v_c} = \bigcap _{\alpha } IV_{\alpha }$$ I v c = ⋂ α I V α for all nonzero fractional ideals I of D. In this paper, among other things, we prove that D is a $$v_c$$ v c -Noetherian domain if and only if D is a Krull domain, if and only if $$v_c = v$$ v c = v and every prime t-ideal of D is a maximal t-ideal. As a corollary, we have that if D is one-dimensional, then $$v_c = v$$ v c = v if and only if D is a Dedekind domain.


2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Qonita Qurrota A'yun ◽  
Sri Wahyuni

Daerah integral R dikatakan perinormal jika untuk setiap overring (lokal) T dari R yang memenuhi kondisi going-down, maka T merupakan lokalisasi dari R pada ideal prima. Perinormalitas merupakan salah satu sifat ketertutupan integral. Dengan memperhatikan bahwa klosur integral dari daerah normal Noether merupakan daerah Krull, akan ditunjukkan bagaimana sifat perinormalitas di daerah Krull.An integral domain R is said to be perinormal if whenever T is a (local) overring of R such that the inclusion R in T satisfies going-down, it follows that T is a localization of R necessarily at a prime ideal. Perinormality is one of integral closedness property. As the integral closure of any Noetherian normal domain is Krull, it will be shown how perinormality behaves on Krull domains.


2020 ◽  
Vol 224 (6) ◽  
pp. 106269
Author(s):  
S. El Baghdadi ◽  
L. Izelgue ◽  
A. Tamoussit
Keyword(s):  

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 47 (5) ◽  
pp. 1917-1929
Author(s):  
Fanggui Wang ◽  
Lei Qiao

2018 ◽  
Vol 70 (6) ◽  
pp. 1284-1318 ◽  
Author(s):  
Alfred Geroldinger ◽  
Qinghai Zhong

AbstractWe introduce a newinvariant describing the structure of sets of lengths in atomicmonoids and domains. For an atomic monoid H, let Δρ(H) be the set of all positive integers d that occur as differences of arbitrarily long arithmetical progressions contained in sets of lengths havingmaximal elasticity ρ(H). We study Δρ(H) for transfer Krull monoids of finite type (including commutative Krull domains with finite class group) with methods from additive combinatorics, and also for a class of weakly Krull domains (including orders in algebraic number fields) for which we use ideal theoretic methods.


2018 ◽  
Vol 44 (1) ◽  
pp. 173-205
Author(s):  
Yusuke Arai ◽  
Ayaka Echizenya ◽  
Kazuhiko Kurano
Keyword(s):  

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