Related papers: Stability result for projective modules over blowu…

We prove that every proper subspace of the moduli space of stable surfaces with fixed volume over an algebraically closed field of characteristic p>5 is projective. As a consequence we also deduce that the same moduli space is projective…

Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…

Let $A$ be a selfinjective algebra over an algebraically closed field. We study the stable dimension of $A$, which is the dimension of the stable module category of $A$ in the sense of Rouquier. Then we prove that $A$ is…

We prove that an algebraic stack with affine stabilizers over an arbitrary base is \'etale-locally a quotient stack around any point with a linearly reductive stabilizer. This generalizes earlier work by the authors of this article (stacks…

In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.

The main result of the paper establishes the irreducibility of a large family of nonzero central charge induced modules over Affine Lie algebras for any non standard parabolic subalgebra. It generalizes all previously known partial results…

An algebra $A$ is said to be directly finite if each left invertible element in the (conditional) unitization of $A$ is right invertible. We show that the reduced group ${\rm C}^\ast$-algebra of a unimodular group is directly finite,…

Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if Ann$(f)+I=R$ for all $f\in I$. If $J$ is the trace of a projective $R$-module $M$, we prove that $J$ is generated by the…

Persistence modules serve as the algebraic foundation for topological data analysis, typically studied as representations of posets over a field. This article extends the structural and decomposition theory of persistence modules to the…

It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…

We investigate the moduli space ${\mathcal P}_g$ of smooth complex projective curves of genus $g$ equipped with a projective structure. When $g\, \geq\, 3$, it is shown that this moduli space ${\mathcal P}_g$ does not admit any nonconstant…

We show that a ring R has stable range one if and only if every left unit lifts modulo every left principal ideal. We also show that a left quasi-morphic ring has stable range one if and only if it is left uniquely generated. Thus we answer…

Let $p \geq 5$ be a prime number and let $G = SL_2(\mathbb{Q}_p)$. Let $\Xi$ = Spec$(Z)$ denote the spectrum of the centre $Z$ of the pro-$p$ Iwahori Hecke algebra of $G$ with coefficients in a field $k$ of characteristic $p$. Let…

Motivated by the goal of studying cluster algebras in infinite type, we study the stability domains of modules for the preprojective algebra in the corresponding infinite types. Specifically, we study real bricks: those modules whose…

Let $(R,\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\ge}-1$ be an integer and $ r=\depth_k(I,N)$ the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M.…

Let $R$ be a commutative ring. Roughly speaking, we prove that an $R$-module $M$ is flat iff it is a direct limit of $R$-module affine algebraic varieties, and $M$ is a flat Mittag-Leffler module iff it is the union of its $R$-submodule…

We provide a certain direct-sum decomposition of reflexive modules over (one-dimensional) Arf local rings. We also see the equivalence of three notions, say, integrally closed ideals, trace ideals, and reflexive modules of rank one (i.e.,…

The asymptotic stability of several homological invariants of the graded pieces of a graded module has attracted quite a lot of attention over the last decades. We provide in this text several stability results together with estimates of…

B. Blackadar recently proved that any full corner $pAp$ in a unital C*-algebra $A$ has K-theoretic stable rank greater than or equal to the stable rank of $A$. (Here $p$ is a projection in $A$, and fullness means that $ApA=A$.) This result…

We study the cancellation property of projective modules of rank $2$ with a trivial determinant over Noetherian rings of dimension $\leq 4$. If $R$ is a smooth affine algebra of dimension $4$ over an algebraically closed field $k$ such that…