Quasi-Duality, Linear Compactness and Morita Duality for Power Series Rings
Canadian mathematical bulletin, Tome 39 (1996) no. 2, pp. 250-256
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AS a generalization of Morita duality, Kraemer introduced the notion of quasi-duality and showed that each left linearly compact ring has a quasi-duality. Let R be an associative ring with identity and R[[x]] the power series ring. We prove that (1) R[[x]] has a quasi-duality if and only if R has a quasi-duality; (2) R[[x]] is left linearly compact if and only if R is left linearly compact and left noetherian; and (3) R[[x]] has a Morita duality if and only if R is left noetherian and has a Morita duality induced by a bimodule RUS such that S is right noetherian.
Xue, Weimin. Quasi-Duality, Linear Compactness and Morita Duality for Power Series Rings. Canadian mathematical bulletin, Tome 39 (1996) no. 2, pp. 250-256. doi: 10.4153/CMB-1996-032-7
@article{10_4153_CMB_1996_032_7,
author = {Xue, Weimin},
title = {Quasi-Duality, {Linear} {Compactness} and {Morita} {Duality} for {Power} {Series} {Rings}},
journal = {Canadian mathematical bulletin},
pages = {250--256},
year = {1996},
volume = {39},
number = {2},
doi = {10.4153/CMB-1996-032-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-032-7/}
}
TY - JOUR AU - Xue, Weimin TI - Quasi-Duality, Linear Compactness and Morita Duality for Power Series Rings JO - Canadian mathematical bulletin PY - 1996 SP - 250 EP - 256 VL - 39 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-032-7/ DO - 10.4153/CMB-1996-032-7 ID - 10_4153_CMB_1996_032_7 ER -
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