In this paper, we introduce a new definition for nilpotent fuzzy subgroups, which is called the good nilpotent fuzzy subgroup or briefly g-nilpotent fuzzy subgroup. In fact, we prove that this ...definition is a good generalization of abstract nilpotent groups. For this, we show that a group G is nilpotent if and only if any fuzzy subgroup of G is a g-nilpotent fuzzy subgroup of G. In particular, we construct a nilpotent group via a g-nilpotent fuzzy subgroup. Finally, we characterize the elements of any maximal normal abelian subgroup by using a g-nilpotent fuzzy subgroup.
In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix B consisting of two Jordan blocks of the same size. ...We list all the possible Jordan canonical forms of the nilpotent matrices that commute with B by characterizing the corresponding partitions.
We will use commutators to provide decompositions of 3×3 matrices as sums whose terms satisfy some polynomial identities, and we apply them to bounded linear operators and endomorphisms of free ...modules of infinite rank. In particular it is proved that every bounded operator of an infinite-dimensional complex Hilbert space is a sum of four automorphisms of order 3 and that every simple ring that is obtained as a quotient of the endomorphism ring of an infinite-dimensional vector space modulo its maximal ideal is a sum of three nilpotent subrings.
The purpose of this work is to give a direct proof of the multiplicative Brunn-Minkowski inequality in nilpotent Lie groups based on Hadwiger-Ohmann's one of the classical Brunn-Minkowski inequality ...in Euclidean space.
Abstract
Building on MacDonald’s formula for the distance from a rank-one projection to the set of nilpotents in
$\mathbb {M}_n(\mathbb {C})$
, we prove that the distance from a rank
$n-1$
projection ...to the set of nilpotents in
$\mathbb {M}_n(\mathbb {C})$
is
$\frac {1}{2}\sec (\frac {\pi }{\frac {n}{n-1}+2} )$
. For each
$n\geq 2$
, we construct examples of pairs
$(Q,T)$
where
Q
is a projection of rank
$n-1$
and
$T\in \mathbb {M}_n(\mathbb {C})$
is a nilpotent of minimal distance to
Q
. Furthermore, we prove that any two such pairs are unitarily equivalent. We end by discussing possible extensions of these results in the case of projections of intermediate ranks.
In this paper, we address a question concerning nilpotent Frobenius actions on Rees algebras and associated graded rings. We prove a nilpotent analog of a theorem of Huneke for Cohen–Macaulay ...singularities. This is achieved by introducing a depth‐like invariant which captures as special cases Lyubeznik's F‐depth and the generalized F‐depth from Maddox–Miller and is related to the generalized depth with respect to an ideal. We also describe several properties of this new invariant and identify a class of regular elements for which weak F‐nilpotence deforms.
Let K be an algebraically closed field of prime characteristic p. If p does not divide n, irreducible modules over sln(K) for regular and subregular nilpotent representations have already known (see ...10 and 9). In this article, we investigate the question when p divides n, and precisely describe simple modules of sln for regular and subregular nilpotent representations.
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