Related papers: Some Maximal Commutative Subrings of M_n(D)
Let $D$ be a division ring with center $F$, and $G$ a subnormal subgroup of $D^*$. We show that if $G$ is a locally solvable group such that $G^{(i)}$ is algebraic over $F$, then $G$ must be central. Also, if $M$ is non-abelian locally…
We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.
The aim of this paper is threefold: first, to prove that the endomorphism ring associated to a pure subring of a regular local ring is a noncommutative crepant resolution if it is maximal Cohen-Macaulay; second, to see that in that…
We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact…
We determine all maximal subgroups of the direct product $\sc G^n$ of $\sc n$ copies of a group~$\sc G$. If $\sc G$ is finite, we show that the number of maximal subgroups of~$\sc G^n$ is a quadratic function of~$\sc n$ if $\sc G$ is…
We study ideal-simple commutative semirings and summarize the results giving their classification, in particular when they are finitely generated. In the principal case of (para)semifields, we then consider their minimal number of…
We introduce a unified theory of Cartan subgroups and maximal toroids - defined as connected multiplicative type subgroups that are maximal amongst all such subgroups - which holds for all affine algebraic groups over a field, regardless of…
If $R$ is a semiartinian Von Neumann regular ring, then the set $\Prim_{R}$ of primitive ideals of $R$, ordered by inclusion, is an artinian poset in which all maximal chains have a greatest element. Moreover, if $\Prim_{R}$ has no infinite…
We define the localisation of a Hilbert module in analogy to the local multiplier algebra. We use properties of this localisation to enrich non-closed actions on $C^*$-algebras to closed actions on local multiplier algebras, and descend…
A classical result due to Morita and Azumaya establishes that given two arbitrary rings, any duality between their finitely generated modules is representable by a faithfully balanced bimodule which is a finitely generated injective…
We construct area-minimizing submanifolds with fractal singular sets on compact Riemannian manifolds. Thus, we settle a conjecture by Almgren and our answer is sharp dimensionwise. Furthermore, we can prescribe arbitrarily the strata in the…
Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.
We describe the endomorphism rings in an additive category whose objects are right $R$-modules $M$ with a fixed chain of submodules $0=M^{(0)}\leq M^{(1)}\leq M^{(2)} \leq \dots \leq M^{(n)}=M$ and the behaviour of these objects as far as…
We give counterexamples to the following conjecture of Auslander: given a finitely generated module $M$ over an Artin algebra $\Lambda$, there exists a positive integer $n_M$ such that for all finitely generated $\Lambda$-modules $N$, if…
Let $\fa$ be an ideal of a Noetherian local ring $(R,\fm)$ and $M$ a finitely generated $R$-module. In this paper we introduce some criterions on Artinianness of formal local cohomology, in particular vanishing and finiteness of local…
By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…
The aim of this paper is to solve a problem proposed by Dominique Bourn: to provide a categorical-algebraic characterisation of groups amongst monoids and of rings amongst semirings. In the case of monoids, our solution is given by the…
Let $\mathcal C$ be the category of finite graphs. Lov\`{a}sz shows that the semi-ring of isomorphism classes of $\mathcal C$ (with coproduct as sum, and product as multiplication) is embedded into the direct product of the semi-ring of…
In the present paper we prove that every 2-local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has an extension to a derivation on the matrix ring over this…
It is proved that the additive group of every semidistributive nearring $R$ with an identity is abelian and if R has no elements of order $2$, then the nearring $R$ actually is an associative ring.