Witt equivalence of semilocal Dedekind domains in global fields

2007 ◽  
Vol 77 (1) ◽  
pp. 1-24 ◽  
Author(s):  
B. Rothkegel ◽  
A. Czogała
Keyword(s):  
Global Fields ◽  
Dedekind Domains ◽  
Witt Equivalence

scholarly journals Witt equivalence of function fields over global fields

2017 ◽  
Vol 369 (11) ◽  
pp. 7861-7881 ◽  
Author(s):  
Paweł Gładki ◽  
Murray Marshall
Keyword(s):  
Function Fields ◽  
Global Fields ◽  
Witt Equivalence

Witt equivalence of global fields

1991 ◽  
Vol 19 (4) ◽  
pp. 1125-1149 ◽  
Author(s):  
Kazimierz Szymiczek
Keyword(s):  
Global Fields ◽  
Witt Equivalence

scholarly journals Witt equivalence of function fields of conics

2020 ◽  
Vol 30 (1) ◽  
pp. 63-78
Author(s):  
P. Gladki ◽  
◽  
M. Marshall
Keyword(s):  
Quadratic Form ◽  
Function Fields ◽  
Local Fields ◽  
Bilinear Forms ◽  
Conic Sections ◽  
Witt Rings ◽  
Global Fields ◽  
Witt Equivalence ◽  
Form Theory ◽  
And Function

Two fields are Witt equivalent if, roughly speaking, they have the same quadratic form theory. Formally, that is to say that their Witt rings of symmetric bilinear forms are isomorphic. This equivalence is well understood only in a few rather specific classes of fields. Two such classes, namely function fields over global fields and function fields of curves over local fields, were investigated by the authors in their earlier works [5] and [6]. In the present work, which can be viewed as a sequel to the earlier papers, we discuss the previously obtained results in the specific case of function fields of conic sections, and apply them to provide a few theorems of a somewhat quantitive flavour shedding some light on the question of numbers of Witt non-equivalent classes of such fields.

Prime uniserial modules and rings

2019 ◽  
Vol 18 (02) ◽  
pp. 1950035 ◽  
Author(s):  
M. Behboodi ◽  
Z. Fazelpour
Keyword(s):  
Commutative Rings ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Direct Sum ◽  
Dedekind Domains ◽  
Prime Submodules ◽  
Uniserial Modules ◽  
Structure Formula

We define prime uniserial modules as a generalization of uniserial modules. We say that an [Formula: see text]-module [Formula: see text] is prime uniserial ([Formula: see text]-uniserial) if its prime submodules are linearly ordered by inclusion, and we say that [Formula: see text] is prime serial ([Formula: see text]-serial) if it is a direct sum of [Formula: see text]-uniserial modules. The goal of this paper is to study [Formula: see text]-serial modules over commutative rings. First, we study the structure [Formula: see text]-serial modules over almost perfect domains and then we determine the structure of [Formula: see text]-serial modules over Dedekind domains. Moreover, we discuss the following natural questions: “Which rings have the property that every module is [Formula: see text]-serial?” and “Which rings have the property that every finitely generated module is [Formula: see text]-serial?”.

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.

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