Factorization of invertible matrices over rings of stable rank one
نویسندگان
چکیده
منابع مشابه
Column-Partitioned Matrices Over Rings Without Invertible Transversal Submatrices
Let the columns of a p× q matrix M over any ring be partitioned into n blocks, M = [M1, . . . , Mn]. If no p × p submatrix of M with columns from distinct blocks Mi is invertible, then there is an invertible p×p matrix Q and a positive integer m ≤ p such that QM = [QM1, . . . , QMn] is in reduced echelon form and in all but at most m − 1 blocks QMi the last m entries of each column are either a...
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Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
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let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1990
ISSN: 0263-6115
DOI: 10.1017/s1446788700029980