1
Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 19395-5746, Iran.
2
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran.
Abstract
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 then characterize submodules of nest modules of matrices over $D$ in terms of certain finite sequences of left row reduced echelon or right column reduced echelon matrices with entries from $D$. We use this result to characterize principal submodules of nest modules. We also describe subbimodules of nest modules of matrices. As a consequence, we characterize (one-sided) ideals of nest algebras of matrices over division rings.
Yahaghi, B. R., & Rahimi-Alangi, M. (2015). On nest modules of matrices over division rings. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 47-63.
MLA
B. R. Yahaghi; M. Rahimi-Alangi. "On nest modules of matrices over division rings". Bulletin of the Iranian Mathematical Society, 41, Issue 7 (Special Issue), 2015, 47-63.
HARVARD
Yahaghi, B. R., Rahimi-Alangi, M. (2015). 'On nest modules of matrices over division rings', Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), pp. 47-63.
VANCOUVER
Yahaghi, B. R., Rahimi-Alangi, M. On nest modules of matrices over division rings. Bulletin of the Iranian Mathematical Society, 2015; 41(Issue 7 (Special Issue)): 47-63.
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