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PP-Rings of Generalized Power Series

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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.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China

    Zhongkui Liu

  2. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

    Javed Ahsan

Authors
  1. Zhongkui Liu
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  2. Javed Ahsan
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Correspondence to Zhongkui Liu.

Additional information

Research supported by National Natural Science Foundation of China, 19501007, and Natural Science Foundation of Gansu, ZQ-96-01

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Liu, Z., Ahsan, J. PP-Rings of Generalized Power Series. Acta Math Sinica 16, 573–578 (2000). https://doi.org/10.1007/s1011400000884

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  • DOI: https://doi.org/10.1007/s1011400000884

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