PP-Rings of Generalized Power Series |
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Authors: | Zhongkui Liu Javed Ahsan |
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Institution: | (1) Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China;(2) Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia |
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Abstract: | Abstract
As a generalization of power series rings, Ribenboim introduced the notion of the rings of generalized power series. Let
R be a commutative ring, and (S, ≤) a strictly totally ordered monoid. We prove that (1) the ring R
S,≤]] of generalized power series is a PP-ring if and only if R is a PP-ring and every S-indexed subset C of B(R) (the set of all idempotents of R) has a least upper bound in B(R) and (2) if (S, ≤) also satisfies the condition that 0 ≤s for any s∈S, then the ring R
S,≤
]] is weakly PP if and only if R is weakly PP.
Research supported by National Natural Science Foundation of China, 19501007, and Natural Science Foundation of Gansu, ZQ-96-01 |
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Keywords: | Ring of generalized power series PP-ring Weakly PP-ring |
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