Related papers: Primeness, semiprimeness and localisation in Iwasa…

This is a survey of the known properties of Iwasawa algebras, which are completed group rings of compact p-adic analytic groups with coefficients the ring Zp of p-adic integers or the field Fp of p elements. A number of open questions are…

Let G be a nilpotent p-valuable (compact p-adic Lie) group. There is an ongoing investigation into the prime ideals of its completed group algebra (Iwasawa algebra), and there remains an open conjecture that they can all be proved to have a…

The set of minimal primes of a ring is a very important set as far the spectrum of a ring is concerned as every prime contains a minimal prime. So, knowing the minimal primes is the first (important and difficult) step in describing the…

In this paper for a noetherian ring R with nilradical N we define semiprime ideals P and Q called as the left and right krull homogenous parts of N . We also recall the known definitions of localisability and the weak ideal invariance…

Let $k$ be a finite field of characteristic $p$, and $G$ a compact $p$-adic analytic group. Write $kG$ for the completed group ring of $G$ over $k$. In this paper, we describe the structure of the ring $kG/P$, where $P$ is a minimal prime…

Noncommutative Iwasawa theory has created a lot of interest in Whitehead groups of Iwasawa algebras of compact p-adic Lie groups with a quotient isomorphic to the additive group of p-adic integers. In this paper we compute Whitehead groups…

Let (T,m) be a complete local (Notherian) ring, C a finite set of pairwise incomparable nonmaximal prime ideals of T, and p a nonzero element. We provide necessary and sufficient conditions for T to be the completion of an integral domain A…

Fix two distinct odd primes $p$ and $q$. We study "$p\ne q$" Iwasawa theory in two different settings. Let $K$ be an imaginary quadratic field of class number 1 such that both $p$ and $q$ split in $K$. We show that under appropriate…

We study prime ideals in skew power series rings $T:=R[[y;\tau,\delta]]$, for suitably conditioned right noetherian complete semilocal rings $R$, automorphisms $\tau$ of $R$, and $\tau$-derivations $\delta$ of $R$. These rings were…

For a prime $p>2$, let $G$ be a semi-simple, simply connected, split Chevalley group over $\mathbb{Z}_p$, $G(1)$ be the first congruence kernel of $G$ and $\Omega_{G(1)}$ be the mod-$p$ Iwasawa algebra defined over the finite field…

This paper contains a detailed exposition of the content of section five in Kakde's paper arXiv:1008.0142. We proceed in a slightly more axiomatic way to pin down the exact requirements on the $p$-adic Lie group under consideration. We also…

Let $G$ be a torsionfree compact $p$-adic analytic group. We give sufficient conditions on $p$ and $G$ which ensure that the Iwasawa algebra $\Omega_G$ of $G$ has no non-trivial two-sided reflexive ideals. Consequently, these conditions…

This paper is lead by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, R of a p-adic analytic group G. For G without any p-torsion element we…

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_\infty and k/Q are finite. We give a full description of the algebraic structure of the semisimple algebra QG=Quot(\Lambda G)…

Necessary and sufficient conditions are given for a prime Noetherian algebra K[S] of a submonoid S of a polycyclic-by-finite group G to be a maximal order. These conditions are entirely in terms of the monoid S. This extends earlier results…

In this paper we give some sufficient and some necessary conditions for an \'etale groupoid algebra to be a prime ring. As an application we recover the known primeness results for inverse semigroup algebras and Leavitt path algebras. It…

We study the arithmetic of seminormal $v$-noetherian weakly Krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes. These monoids include seminormal orders in holomorphy rings in global…

We completely calculate the Fitting ideal of the classical $p$-ramified Iwasawa module for any abelian extension $K/k$ of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former…

We consider properties of extensions of Krull domains such as flatness that involve behavior of extensions and contractions of prime ideals. Let (R,m) be an excellent normal local domain with field of fractions K, let y be a nonzero element…

Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally…