一些半环半模对  

Some semiring-semimodule pairs

作　　者：冯立[1] 杨琳[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纺织高校基础科学学报》2009年第4期523-528,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(10471112);陕西省自然科学专项基金资助项目(05A15);陕西省教育厅自然科学专项基金资助项目(07JK413)

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.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.

关 键 词：双弱归纳半环半模对 双＊-μ-半环半模对 双＊-λ-半环半模对 形式幂级数半环半模对 

分 类 号：O152.7[理学—数学]