منابع مشابه
Inversion of Matrices over a Commutative Semiring
It is a well-known consequence of the elementary theory of vector spaces that if A and B are n-by-n matrices over a field (or even a skew field) such that AB = 1, then BA = 1. This result remains true for matrices over a commutative ring, however, it is not, in general, true for matrices over noncommutatives rings. In this paper we show that if A and B are n-by-n matrices over a commutative sem...
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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 Algebra
سال: 1970
ISSN: 0021-8693
DOI: 10.1016/0021-8693(70)90084-0