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中文摘要：
研究了双弱归纳半环半模对,双＊-μ-半环半模对和双＊-λ-半环半模对.讨论了系数在一些半环半模对中的形式幂级数半环半模对,证明了系数为双归纳半环半模对的形式幂级数半环半模对（双μ-半环半模对,双＊-μ-半环半模对,双λ-半环半模对,双＊-λ-半环半模对）仍然是双归纳半环半模对（双μ-半环半模对,双＊-μ-半环半模对,双λ-半环半模对,双＊-λ-半环半模对）,给出了系数为双弱归纳半环半模对的形式幂级数半环半模对仍然是双弱归纳半环半模对的充要条件.
英文摘要：
Bi-weak inductive semiring-semimodule pairs, bi-＊-μ-semiring semimodule pairs and bi- ＊ -λ-semiring-semimodule pairs are studied. Also, the semiring-semimodule pairs of formal power series with coefficients in such a semiring-semimodule pairs is discussed. It is proved that the semiringsemimodule pairs of formal power series with coefficients in bi-inductive semiring semimodule pairs（ b-μ-semiring-semimodule pairs, bi-＊-μ-semi- ring-semimodule pairs, bi-λ-semiring-semimodule pairs and bi- ＊ -λ-semiring-semimodule pairs）are also bi-inductive semiring-semimodule pairs （bi-μ-semiring-semimodule pairs, bi-＊-μ-semiring-semimodule pairs, bi-λ-semiring-semimodule pairs and bi- ＊ -λ-semiring-semimodule pairs, respectively ）. The semiring-semimodule pairs of formal power series with coefficients in bi-weak inductive semiring-semimodule pairs are also bi-weak inductive semiring-semimodule and its necessary and sufficient conditions are given.
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