ON QUASI-GALOIS EXTENSIONS OF DIVISION RINGS
نویسندگان
چکیده
منابع مشابه
On the Galois Theory of Division Rings
1. Throughout this paper, K will represent a division ring and L a galois division subring. We are interested in establishing a galois theory for the extension K/L when K/L is locally finite. In order to do this one must identify the galois subrings of K containing L. An example given by Jacobson [4] shows that not every such division subring is galois. However, we obtain that each subring subj...
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 کاملOn Azumaya Galois Extensions and Skew Group Rings
Two characterizations of an Azumaya Galois extension of a ring are given in terms of the Azumaya skew group ring of the Galois group over the extension and a Galois extension of a ring with a special Galois system is determined by the trace of the Galois group.
متن کاملCENTRAL EXTENSIONS OF n–ORDERED DIVISION RINGS
We study central extensions of division rings with orderings of higher level. We show that orderings extend to certain immediate and inert extensions. Further, it is proved that any n–ordered division ring can be extended to a n–ordered division ring with almost real closed center. In the last section an old theorem due to Neumann is generalized: every n–ordered division ring can be extended to...
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: Hokkaido Mathematical Journal
سال: 1963
ISSN: 0385-4035
DOI: 10.14492/hokmj/1530691329