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pro vyhledávání: '"Paul J. Truman"'
Autor:
Paul J. Truman
Publikováno v:
Proceedings of the Edinburgh Mathematical Society. :1-17
The Hopf–Galois structures admitted by a Galois extension of fields $ L/K $ with Galois group G correspond bijectively with certain subgroups of $ \mathrm{Perm}(G) $ . We use a natural partition of the set of such subgroups to obtain a method for p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b5d9748eab7a758581029f7520d4e1da
https://doi.org/10.1017/s0013091523000184
https://doi.org/10.1017/s0013091523000184
Publikováno v:
Communications in Algebra. 47:2086-2101
Every Hopf-Galois structure on a finite Galois extension $K/k$ where $G=Gal(K/k)$ corresponds uniquely to a regular subgroup $N\leq B=\operatorname{Perm}(G)$, normalized by $\lambda(G)\leq B$, in accordance with a theorem of Greither and Pareigis. Th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::094d83f9f7072184b79f746bf4f19577
https://doi.org/10.1080/00927872.2018.1529237
https://doi.org/10.1080/00927872.2018.1529237
Autor:
Alan Koch, Kevin Keating, Cornelius Greither, Paul J. Truman, Lindsay N. Childs, Robert Underwood, Timothy Kohl
Publikováno v:
Mathematical Surveys and Monographs ISBN: 9781470467371
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9d5c3badc2281e47700b95d718898a3d
https://doi.org/10.1090/surv/260
https://doi.org/10.1090/surv/260
Autor:
Lindsay N. Childs, Cornelius Greither, Kevin P. Keating, Alan Koch, Timothy Kohl, Paul J. Truman, Robert G. Underwood
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be vie
Autor:
Paul J. Truman, Alan Koch
Given a skew left brace $\mathfrak{B}$, we introduce the notion of an "opposite" skew left brace $\mathfrak{B}'$, which is closely related to the concept of the opposite of a group, and provide several applications. Skew left braces are closely linke
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fccc0377fab88407448777720de251ab
http://arxiv.org/abs/1908.02682
http://arxiv.org/abs/1908.02682
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9783030115203
We discuss isomorphism questions concerning the Hopf algebras that yield Hopf–Galois structures for a fixed separable field extension L/K. We study in detail the case where L/K is Galois with dihedral group \(D_p\), \(p\ge 3\) prime and give explic
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::079b4c079438146329b850c7d7dce921
Autor:
Paul J. Truman
We prove three theorems concerning the Hopf-Galois module structure of fractional ideals in a finite tamely ramified extension of $ p $-adic fields or number fields which is $ H $-Galois for a commutative Hopf algebra $ H $. Firstly, we show that if
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b59d2aa7d29ee08791b0471a8350fd82
Autor:
Paul J. Truman
Publikováno v:
Communications in Algebra. 44:1119-1130
Let L/K be a finite Galois extension of local or global fields in any characteristic with nonabelian Galois group G, and let 𝔅 be an ambiguous ideal of L. We show that 𝔅 is free over its associated order in K[G] if and only if it is free over i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6d0afa52cb4622fdc3312ee66c5a8044
https://doi.org/10.1080/00927872.2014.999930
https://doi.org/10.1080/00927872.2014.999930
Autor:
Paul J. Truman
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 28:557-582
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2ae0d2f354f6b4383c000e610c5f4e79
https://doi.org/10.5802/jtnb.953
https://doi.org/10.5802/jtnb.953
Let $ L/K $ be a finite separable extension of fields whose Galois closure $ E/K $ has group $ G $. Greither and Pareigis have used Galois descent to show that a Hopf algebra giving a Hopf-Galois structure on $ L/K $ has the form $ E[N]^{G} $ for som
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd3abf9d095def5d128a2c124221dd56