scholarly journals Ehrhart Series, Unimodality, and Integrally Closed Reflexive Polytopes

2016 ◽  
Vol 20 (4) ◽  
pp. 705-717 ◽  
Author(s):  
Benjamin Braun ◽  
Robert Davis
Keyword(s):  
Reflexive Polytopes ◽  
Ehrhart Series ◽  
Integrally Closed

scholarly journals An Ehrhart Series Formula For Reflexive Polytopes

10.37236/1153 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Benjamin Braun
Keyword(s):  
Ehrhart Polynomial ◽  
Lattice Polytopes ◽  
Reflexive Polytopes ◽  
Ehrhart Series ◽  
Multiplicative Relationship ◽  
Free Sum

It is well known that for $P$ and $Q$ lattice polytopes, the Ehrhart polynomial of $P\times Q$ satisfies $L_{P\times Q}(t)=L_P(t)L_Q(t)$. We show that there is a similar multiplicative relationship between the Ehrhart series for $P$, for $Q$, and for the free sum $P\oplus Q$ that holds when $P$ is reflexive and $Q$ contains $0$ in its interior.

scholarly journals $$v_c$$-Noetherian domains and Krull domains

2021 ◽  
Author(s):  
Gyu Whan Chang
Keyword(s):  
Dedekind Domain ◽  
Closed Domain ◽  
One Dimensional ◽  
Star Operation ◽  
Krull Domain ◽  
Noetherian Domain ◽  
Integrally Closed ◽  
Krull Domains

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.

scholarly journals Integrally closed factor domains

1988 ◽  
Vol 37 (3) ◽  
pp. 353-366 ◽  
Author(s):  
Valentina Barucci ◽  
David E. Dobbs ◽  
S.B. Mulay
Keyword(s):  
Prime Ideal ◽  
The Other ◽  
Integral Domains ◽  
Other Hand ◽  
Dedekind Domains ◽  
Integrally Closed

This paper characterises the integral domains R with the property that R/P is integrally closed for each prime ideal P of R. It is shown that Dedekind domains are the only Noetherian domains with this property. On the other hand, each integrally closed going-down domain has this property. Related properties and examples are also studied.

Graded integral domains in which each nonzero homogeneous t-ideal is divisorial

2019 ◽  
Vol 18 (01) ◽  
pp. 1950018 ◽  
Author(s):  
Gyu Whan Chang ◽  
Haleh Hamdi ◽  
Parviz Sahandi
Keyword(s):  
Integral Domain ◽  
Nonzero Ideal ◽  
Integral Domains ◽  
Cancellative Monoid ◽  
Integrally Closed ◽  
Graded Integral Domain

Let [Formula: see text] be a nonzero commutative cancellative monoid (written additively), [Formula: see text] be a [Formula: see text]-graded integral domain with [Formula: see text] for all [Formula: see text], and [Formula: see text]. In this paper, we study graded integral domains in which each nonzero homogeneous [Formula: see text]-ideal (respectively, homogeneous [Formula: see text]-ideal) is divisorial. Among other things, we show that if [Formula: see text] is integrally closed, then [Formula: see text] is a P[Formula: see text]MD in which each nonzero homogeneous [Formula: see text]-ideal is divisorial if and only if each nonzero ideal of [Formula: see text] is divisorial, if and only if each nonzero homogeneous [Formula: see text]-ideal of [Formula: see text] is divisorial.

scholarly journals NORMAL DOMAINS WITH MONOMIAL PRESENTATIONS

2009 ◽  
Vol 19 (03) ◽  
pp. 287-303 ◽  
Author(s):  
ISABEL GOFFA ◽  
ERIC JESPERS ◽  
JAN OKNIŃSKI
Keyword(s):  
Commutative Algebra ◽  
Class Group ◽  
Semigroup Algebra ◽  
Closed Domain ◽  
Finitely Generated ◽  
Defining Relations ◽  
Integrally Closed ◽  
Algebra Over A Field

Let A be a finitely generated commutative algebra over a field K with a presentation A = K 〈X1,…, Xn | R〉, where R is a set of monomial relations in the generators X1,…, Xn. So A = K[S], the semigroup algebra of the monoid S = 〈X1,…, Xn | R〉. We characterize, purely in terms of the defining relations, when A is an integrally closed domain, provided R contains at most two relations. Also the class group of such algebras A is calculated.

Completely integrally closed modules and rings

2010 ◽  
Vol 171 (2) ◽  
pp. 296-306 ◽  
Author(s):  
A. A. Tuganbaev
Keyword(s):  
Integrally Closed
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