Related papers: Endomorphism rings via minimal morphisms

Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known…

We describe the automorphism group of the endomorphism semigroup $\End(K[x_1,...,x_n])$ of ring $K[x_1,...,x_n]$ of polynomials over an {\it arbitrary} field $K$. A similar result is obtained for automorphism group of the category of…

In this paper we show that for any affine complete rational surface singularity there is a correspondence between the dual graph of the minimal resolution and the quiver of the endomorphism ring of the special CM modules. We thus call such…

We give a proof of a Conjecture of Walker which states that one can recover the lengths of the bars of a circular linkage from the cohomology ring of the configuration space. For a large class of length vectors, this has been shown by…

Let $R$ be a commutative ring with identity. The ring $R\times R$ can be viewed as an extension of $R$ via the diagonal map $\Delta: R \hookrightarrow R\times R$, given by $\Delta(r) = (r, r)$ for all $r\in R$. It is shown that, for any $a,…

$\newcommand{\OO}[1]{\mathcal{O}_{#1}}\newcommand{\GG}{\mathcal{G}}\newcommand{\End}{\mathrm{End}}\newcommand{\O}{\mathcal{O}}$Let $K/F$ be a quadratic extension of non-Archimedean local fields of characteristic not equal to 2, with rings…

We study a class of $\Z^{d}$-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of $\Z^{d}$. We prove that any measurable factor map and even…

Let $M$ be a compact $n$-dimensional Riemanian manifold, End($M$) the set of the endomorphisms of $M$ with the usual $\mathcal{C}^0$ topology and $\phi: M\to\mathbb{R}$ continuous. We prove that there exists a dense subset of $\mathcal{A}$…

If $\pi:(X,T)\to(Z,S)$ is a topological factor map between uniquely ergodic topological dynamical systems, then $(X,T)$ is called an isomorphic extension of $(Z,S)$ if $\pi$ is also a measure-theoretic isomorphism. We consider the case when…

Let $M$ and $N$ be compact smooth oriented Riemannian $n$-manifolds without boundary embedded in $\mathbb{R}^{n+1}$. Several problems about minimal distortion bending and morphing of $M$ to $N$ are posed. Cost functionals that measure…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

Let $A\subset B$ be an integral ring extension of integral domains with fields of fractions $K$ and $L$, respectively. The integral degree of $A\subset B$, denoted by ${\rm d}_A(B)$, is defined as the supremum of the degrees of minimal…

In this paper we study maximal subrings up to isomorphism of fields. It is shown that each field with zero characteristic has infinitely many maximal subrings up to isomorphism. If $K$ is an algebraically closed field and $x$ is an…

Given two seprable irreducible polynomials $P_1$ and $P_2$ over a filed $\mathbb{K}$. We show that the rings $\mathbb{K}[X]/(P_1^n)$ and $\mathbb{K}[X]/(P_2^n)$ are isomorphic if and only if their residue fields $\mathbb{K}[X]/(P_1)$ and…

Let $\Lambda$ be a commutative local uniserial ring of length at least seven with radical factor ring $k$. We consider the category $S(\Lambda)$ of all possible embeddings of submodules of finitely generated $\Lambda$-modules and show that…

If $M$ is an $R$-module, we study the submodules $K\leq M$ with the property that $K$ is invariant with respect to all monomorphisms $K\rightarrow M$. Such submodules are called \textsl{strictly invariant}. For the case of $%…

We prove that a quasi-finite endomorphism of an algebraic variety over an algebraically closed field of characteristic zero, that is injective on the complement of a closed subvariety, is an automorphism. We also prove that an endomorphism…

We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is…

Given the action of a group $G$ on a set $X$, an endomorphism of $X$ is a function $f:X \rightarrow X$ which is $G$-equivariant, that is, it commutes with the action, i.e., $f(g\cdot x)= g\cdot f(x)$, for all $x\in X$. The set of…

We prove a non-linear version of a theorem of Grayson which is an analogue of the Fundamental Theorem of Algebraic $K$-theory and identify the $K$-theory of the endomorphism category over a space $X$ in terms of reduced $K$-theory of a…