scholarly journals Class groups of maximal orders over Krull domains

1984 ◽  
Vol 31 (1-3) ◽  
pp. 91-107
Author(s):  
L. Le Bruyn
Keyword(s):  
Class Groups ◽  
Maximal Orders ◽  
Krull Domains

Brauer Groups, Class Groups and Maximal Orders for a Krull Scheme

1982 ◽  
Vol 34 (4) ◽  
pp. 996-1010 ◽  
Author(s):  
Heisook Lee ◽  
Morris Orzech
Keyword(s):  
Exact Sequence ◽  
Monoidal Categories ◽  
Brauer Groups ◽  
Class Groups ◽  
Maximal Orders ◽  
Image Position ◽  
Exact Sequences ◽  
Krull Domains

In a previous paper [13] one of us considered Brauer groups Br(C) and class groups Cl(C) attached to certain monoidal categories C of divisorial R-lattices. That paper showed that the groups arising for a suitable pair of categories C1 ⊆ C2 could be related by a tidy exact sequenceIt was shown that this exact sequence specializes to a number of exact sequences which had formerly been handled separately. At the same time the conventional setting of noetherian normal domains was replaced by that of Krull domains, thus generalizing previous results while also simplifying the proofs. This work was carried out in an affine setting, and one aim of the present paper is to carry these results over to Krull schemes. This will enable us to recover the non-affine version of an exact sequence obtained by Auslander [1, p. 261], as well as to introduce a new, non-affine version of a different sequence derived by the same author [2, Theorem 1].

scholarly journals Maximal orders over Krull domains

1968 ◽  
Vol 10 (3) ◽  
pp. 321-332 ◽  
Author(s):  
Robert M Fossum
Keyword(s):  
Maximal Orders ◽  
Krull Domains

The Nielsen-Thurston Classification

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Hyperbolic Geometry ◽  
Mapping Class Groups ◽  
Classification Theorem ◽  
Mapping Class ◽  
Fundamental Result ◽  
Class Groups ◽  
Mapping Torus ◽  
Higher Genus ◽  
Manifold Theory

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². It then states the Nielsen–Thurston classification theorem in various forms, as well as a connection to 3-manifold theory, along with Thurston's geometric classification of mapping torus. The rest of the chapter is devoted to Bers' proof of the Nielsen–Thurston classification. The collar lemma is highlighted as a new ingredient, as it is also a fundamental result in the hyperbolic geometry of surfaces.

Divisibility Properties of Graded Domains

1982 ◽  
Vol 34 (1) ◽  
pp. 196-215 ◽  
Author(s):  
D. D. Anderson ◽  
David F. Anderson
Keyword(s):  
Integral Domain ◽  
Homogeneous Element ◽  
Carry Over ◽  
Divisibility Properties ◽  
Krull Domains

Let R = ⊕α∊гRα be an integral domain graded by an arbitrary torsionless grading monoid Γ. In this paper we consider to what extent conditions on the homogeneous elements or ideals of R carry over to all elements or ideals of R. For example, in Section 3 we show that if each pair of nonzero homogeneous elements of R has a GCD, then R is a GCD-domain. This paper originated with the question of when a graded UFD (every homogeneous element is a product of principal primes) is a UFD. If R is Z+ or Z-graded, it is known that a graded UFD is actually a UFD, while in general this is not the case. In Section 3 we consider graded GCD-domains, in Section 4 graded UFD's, in Section 5 graded Krull domains, and in Section 6 graded π-domains.

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiuya Wang
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Groups ◽  
Upper Bound ◽  
Abelian Groups ◽  
Class Groups ◽  
Abelian Extensions ◽  
Pointwise Bound ◽  
First Case

AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\ell}-torsion in class groups of every A-extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group G, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>1}. When r is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

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.

Social Class and Code Elaboration in Oral Communication

1971 ◽  
Vol 14 (2) ◽  
pp. 421-427 ◽  
Author(s):  
Millicent E. Poole ◽  
T. W. Field
Keyword(s):  
Social Class ◽  
Middle Class ◽  
Working Class ◽  
Oral Communication ◽  
Class Groups ◽  
Parental Occupation ◽  
The Social ◽  
Linguistic Coding

The Bernstein thesis of elaborated and restricted coding orientation in oral communication was explored at an Australian tertiary institute. A working-class/middle-class dichotomy was established on the basis of parental occupation and education, and differences in overall coding orientation were found to be associated with social class. This study differed from others in the area in that the social class groups were contrasted in the totality of their coding orientation on the elaborated/restricted continuum, rather than on discrete indices of linguistic coding.

Sign in / Sign up

Export Citation Format

Share Document