Zobrazeno 1 - 10
of 120
pro vyhledávání: '"Vasiu, Adrian"'
We reobtain and often refine prior criteria due to Kaplansky, McGovern, Roitman, Shchedryk, Wiegand, and Zabavsky--Bilavska and obtain new criteria for a Hermite ring to be an \textsl{EDR}. We mention three criteria: (1) a Hermite ring $R$ is an \tex
Externí odkaz:
http://arxiv.org/abs/2405.01234
A unimodular $2\times 2$ matrix $A$ with entries in a commutative ring $R$ is called weakly determinant liftable if there exists a matrix $B$ congruent to $A$ modulo $R\det(A)$ and $\det(B)=0$; if we can choose $B$ to be unimodular, then $A$ is calle
Externí odkaz:
http://arxiv.org/abs/2404.17656
A unimodular $2\times 2$ matrix with entries in a commutative $R$ is called extendable (resp.\ simply extendable) if it extends to an invertible $3\times 3$ matrix (resp.\ invertible $3\times 3$ matrix whose $(3,3)$ entry is $0$). We obtain necessary
Externí odkaz:
http://arxiv.org/abs/2404.05780
We prove that for all integers $k \geq 1$, $q\ge (k-1)^4+ 6k$, and $m \geq 1$, every matrix in $ M_m(\mathbb F_q)$ is a sum of two kth powers: $M_m(\mathbb F_q)=\{A^k+B^k|A,B\in M_m(\mathbb F_q)\}$. We further generalize and refine this result in the
Externí odkaz:
http://arxiv.org/abs/2306.06588
We introduce the class E2 (resp. SE2) of commutative rings R with the property that each unimodular 2 x 2 matrix with entries in R extends to an invertible 3 x 3 matrix (resp. invertible 3 x 3 matrix whose (3, 3) entry is 0). Among noetherian domains
Externí odkaz:
http://arxiv.org/abs/2303.08413
Autor:
Buium, Alexandru, Vasiu, Adrian
Let $p$ be a prime, let $N\geq 3$ be an integer prime to $p$, let $R$ be the ring of $p$-typical Witt vectors with coefficients in an algebraic closure of $\mathbb F_p$, and consider the correspondence $\mathcal A'_{g,1,N,R}\rightrightarrows \mathcal
Externí odkaz:
http://arxiv.org/abs/2208.00286
Autor:
Loverro, Micah, Vasiu, Adrian
Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over $K:=\text{Frac
Externí odkaz:
http://arxiv.org/abs/2208.00282
Publikováno v:
In Journal of Pure and Applied Algebra July 2024 228(7)
Autor:
Gabber, Ofer, Vasiu, Adrian
Let $p$ be a prime. Let $R$ be a regular local ring of dimension $d\ge 2$ whose completion is isomorphic to $C(k)[[x_1,\ldots,x_d]]/(h)$, with $C(k)$ a Cohen ring with the same residue field $k$ as $R$ and with $h\in C(k)[[x_1,\ldots,x_d]]$ such that
Externí odkaz:
http://arxiv.org/abs/1809.05141
Autor:
Li, Jinghao, Vasiu, Adrian
Publikováno v:
Tunisian J. Math. 1 (2019) 519-538
Let $p$ be a prime. Let $n\in\mathbb N-\{0\}$. Let $\mathcal C$ be an $F^n$-crystal over a locally noetherian $\mathbb F_p$-scheme $S$. Let $(a,b)\in\mathbb N^2$. We show that the reduced locally closed subscheme of $S$ whose points are exactly those
Externí odkaz:
http://arxiv.org/abs/1801.09593