Cyclic Galois extensions of regular local rings
نویسندگان
چکیده
منابع مشابه
Simultaneous Surface Resolution in Cyclic Galois Extensions
We show that simultaneous surface resolution is not always possible in a cyclic extension whose degree is greater than three and is not divisible by the characteristic. This answers a recent question of Ted Chinburg. Section 1: Introduction Let K be a two dimensional algebraic function field over an algebraically closed ground field k. Recall that K/k has a minimal model means that amongst all ...
متن کاملExtensions of Regular Rings
Let $R$ be an associative ring with identity. An element $x in R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if there exist $g in G$, $n in mathbb{Z}$ and $r in R$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). A ring $R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if every element of $R$ is $mathbb{Z}G$-regular (resp. strongly $...
متن کاملCommutative Regular Rings without Prime Model Extensions
It is known that the theory K of commutative regular rings with identity has a model completion K . We show that there exists a countable model of K which has no prime extension to a model of K'. If K and K ate theories in a first order language L, then K is said to be a model completion of K if K extends K, every model of K can be embedded in a model of K , and for any model A of K and models ...
متن کاملOn Certain Classes of Galois Extensions of Rings
Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois extensions. Moreover, it is shown that the intersection of the class of CP-Galois extensions and the class of faithfully Galois extensions is the class of Azumaya Galois extensions.
متن کاملOn a notion of “Galois closure” for extensions of rings
where a ∈ A and j ∈ {1, 2, . . . , n}. Note that the symmetric group Sn naturally acts on A⊗n by permuting the tensor factors, and the ideal I(A,B) ⊂ A⊗n is preserved under this Sn-action. We are interested in imposing on A⊗n the relations in I(A,B) defined by (2) because they are precisely the relations that the conjugates a(i) of a generic element a in a separable field extension of degree n ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1989
ISSN: 0018-2079
DOI: 10.32917/hmj/1206129391