All Questions
8 questions with no upvoted or accepted answers
7
votes
0
answers
226
views
Decomposing an endomorphism as a tensor product
$\DeclareMathOperator\End{End}$Let $f$ be an endomorphism of the finite-dimensional vector space $V$, over the field $K$. The question of whether $f$ is decomposable, that is, whether $V$ can be ...
- 2,287
3
votes
0
answers
474
views
Jacobson-Bourbaki correspondence
The Jacobson-Bourbaki correspondence induces the traditional, finite Galois correspondence by suitable restriction; I've been pondering two things: 1. Are there any (other) interesting applications of ...
3
votes
0
answers
473
views
Infinite Galois correspondence "according to Artin"
Ever since Artin's lectures on Galois Theory one knows how to set up and derive the usual Galois correspondence in the finite(-dimensional) case using just a bit of elementary Linear Algebra, and ...
2
votes
0
answers
60
views
Linearity of a canonical morphism related to scalar extension and coextension
Let $h\colon R\rightarrow S$ be a morphism of commutative ring. Let $M$ and $N$ be $R$-modules. We consider the canonical morphism of $R$-modules $$p\colon{\rm Hom}_R(S\otimes_RM,N)\rightarrow{\rm Hom}...
- 6,700
1
vote
0
answers
37
views
Bounding the length of an R-module of matrices
Loosely related to this: Bounding the length in a module of evaluated skew polynomials
Let $C$ be an $\mathbb{F}_q$-vector subspace of $m \times n$ matrices over $\mathbb{F}_q$. Assume WLOG that $m \...
- 223
1
vote
0
answers
60
views
Bounding the length in a module of evaluated skew polynomials
Let $R$ be a finite principal ideal ring, $S$ a Galois extension of $R$ of degree $m$ (so in particular $S$ is a free $R$-module of rank $m$, and we have an $R$-module isomorphism $S^n \cong \...
- 223
1
vote
0
answers
145
views
Has anyone studied this possible generalisation of the Singular Value Decomposition to all commutative $*$-rings?
I don't know any abstract algebraists personally, which is why I'm asking this question here.
Let $(R,*)$ be a commutative $*$-ring where $*:R \to R$ is an involution. Each conjecture below is stated ...
- 4,943
1
vote
0
answers
95
views
Is it true that the generator of maximal ideal in $M_n(P[x])$ can be choosen to be monic?
Let $P$ be a finite field and $R=M_n(P[x])$ be a matrix polynomial ring.
I want to prove
that for every polynomial (not necessary with invertible leading term) $A(x)\in R$ such that $R\cdot A(x)$ is ...
