关于拟主k-投射半模的进一步结果(英文)  

Further results on quasi-principally k-projective semimodules

作　　者：王秀丽[1] 周茂袁[1,2] 陈志寅[3] 王洪艳 

机构地区：[1]中国民航大学理学院,天津300300 [2]南开大学数学科学学院,天津300071 [3]南开大学组合数学中心,天津300071 [4]长春第二十九中学,长春130013

出　　处：《黑龙江大学自然科学学报》2012年第3期332-334,338,共4页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Science Foundations of Tianjin(08JCYBJC13900);the Civil Aviation University of China(2010kys06)

摘　　要：在k-投射半模和拟主模的理论基础之上,引进拟主k-投射半模的概念,得到关于拟主k-投射半模的几个性质,这是环中拟主模和半环中k-投射半模性质的推广。证明:如果P是一个正则半模,则它是拟主k-投射半模当且仅当它是投射半模。给出在完全可吸收可消去半环上与拟主k-投射半模等价的两个条件。The concept of quasi-principally k-projective semimodules is given on the basis of the theo- ries of k-projective semimodules and quasi-principally modules. Several properties of quasi-principally k- projective semimodules are investigated, which are generalization of the properties of quasi-principally mod- ules of rings and k-projective semimodules of semiring. It is shown that if P is a k-regular semimodule, then P is quasi-principally k-projective if and only if P is projective. And two equivalent conditions to qua- si-principally k-projective semimodules on a eancellative completely subtractive semiring R are given.

关 键 词：可吸收半模 k-正则同态 拟主k-投射半模 自由半模 真正合列 

分 类 号：O153.3[理学—数学]