TY - JOUR ID - 721 TI - On nest modules of matrices over division rings JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Yahaghi, B. R. AU - Rahimi-Alangi, M. AD - Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 19395-5746, Iran. AD - Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran. Y1 - 2015 PY - 2015 VL - 41 IS - Issue 7 (Special Issue) SP - 47 EP - 63 KW - Bimodule of rectangular matrices over a division ring KW - (left/right) submodule KW - subbimodule KW - (one-sided) ideal KW - nest modules DO - N2 - 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. UR - http://bims.iranjournals.ir/article_721.html L1 - http://bims.iranjournals.ir/article_721_5f9a18056601fd0fd44a34d75a22addd.pdf ER -