Morita Duality for the Rings of Generalized Power Series |
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| Authors: | Zhong Kui Liu |
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| Affiliation: | (1) Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China E-mail: liuzk@nwnu.edu.cn, CN |
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| Abstract: | Let A, B be associative rings with identity, and (S, ≤) a strictly totally ordered monoid which is also artinian and finitely generated. For any bimodule A M B , we show that the bimodule [[ AS,≤ ]][M S ,≤][[ BS, ≤ ]] defines a Morita duality if and only if A M B defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring [[A S ,≤]] of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule A M B such that B is right noetherian. Received April 13, 1999, Accepted December 12, 1999 |
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| Keywords: | Morita duality Left linearly compact module Ring of generalized power series |
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