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The Geometric Invariants of Group Extensions
The Geometric Invariants Group Extensions Group Theory
2012/6/30
In this paper, we compute the {\Sigma}^n(G) and {\Omega}^n(G) invariants when 1 \rightarrow H \rightarrow G \rightarrow K \rightarrow 1 is a short exact sequence of finitely generated groups with K fi...
On pro-$p$ analogues of limit groups via extensions of centralizers
Group Theory extensions of centralizers limit groups pro-$p$ analogues
2011/9/5
Abstract: We begin a study of a pro-$p$ analogue of limit groups via extensions of centralizers and call $\mathcal{L}$ this new class of pro-$p$ groups. We show that the pro-$p$ groups of $\mathcal{L}...
Abstract: In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups ca...
Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions
Non-linear Group Polynomial Invariant Rings
2010/11/24
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
Universal central extensions of twisted forms of split simple Lie algebras over rings
Universal central extensions Lie algebras
2010/11/23
We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central exten...
In this paper the concept of the extensions of intuitionistic fuzzy ideals in a semigroup has been extended to a {\Gamma}-Semigroups. Among other results characterization of prime ideals in a {\Gamma...
Valuation Extensions of Algebras Defined by Monic Gröbner Bases
Algebras Defined Monic Grö bner Bases
2010/11/18
Let $K$ be a field, $\mathcal {O}_v$ a valuation ring of $K$ associated to a valuation $v$: $K\rightarrow\Gamma\cup\{\infty\}$, and ${\bf m}_v$ the unique maximal ideal of $\mathcal {O}_v$. Consider ...
We construct an extension $E(A,G)$ of a given group $G$ by infinite non-Archimedean words over an discretely ordered abelian group like $Z^n$. This yields an effective and uniform method to study var...
Seminar Notes on Open Questions in Iwasawa Theory - SNOQIT I: The $\Lambda[ G ]$-modules of Iwasawa theory II: Units and Kummer theory in Iwasawa extensions
11R23 Iwasawa Theory 11R27 Units
2010/12/9
For = Zp[[T ]], the ring of formal power series in one variable, the structure of the finitely generated - torsion modules is a main concern of Iwasawa theory. In this first part of Snoqit1 we inv...
A note on $(\alpha, \beta)$-higher derivations and their extensions to modules of quotients
derivation higher derivation ring of quotients module of quotients
2010/12/3
We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of ( , )-derivation to ( , )-higher derivation and demonstrate that a filter of a...
Artin-Schreier extensions in NIP and simple fields
Artin-Schreier extensions NIP simple fields
2010/12/14
We show that NIP fields have no Artin-Schreier extension, and that simple fields have only a finite number of them.
Extensions of Toric Varieties
toric variety Hilbert function of a local ring tangent cone syzygy
2010/11/29
In this paper, we introduce the notion of “extension” of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being...
本文中我们对于分次代数引入了t-fold模范畴，这是分次模范畴的全子范畴。我们证明了t-fold模范畴在模扩张以及在单射的余核下封闭。利用此性质，我们证明了t-Koszul模范畴也在模扩张以及在单射的余核下封闭。我们给出了代数的单点扩张成为t-Koszul代数的一个充分必要条件。对于单点扩张代数，我们还研究了可线性表现模范畴与其子范畴t-Koszul模范畴相重合的条件。
Commutative Quartic P-Galois Extensions Over a Field of Characteristic Not 2
Galois extension P-Galois extension quartic extension
2010/2/26
In [2], K. Kishimoto introduced the notion of P-Galois extensions and gave some fundamental properties of these extensions. P-Galois extensions relate Hopf Galois extensions, and the author treated th...