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Quasi-Duality, Linear Compactness and Morita Duality for Power Series Rings

Published online by Cambridge University Press:  20 November 2018

Weimin Xue
Weimin Xue*
Affiliation:
Department of Mathematics, Fujian Normal University, Fuzhou, Fujian 350007, People's Republic of China
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Abstract

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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.

Keywords

16D9016P40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 250 - 256
Copyright
Copyright © Canadian Mathematical Society 1996

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