摘要
给出p-内射半模的概念,并在此基础上刻划了p-内射半模与Hom函子的关系.接下来证得p-内射半模的直积与直和仍保持是p-内射半模。以及讨论了在无零因子半环中,p-内射半模与可除半模的关系。最后由于p-内射半模定义的条件比内射半模弱,证明了在任意真半环上存在非零的p-内射半模。
The relationship between p-injective semimodules and HomR（-,E） was introduced based on the notion of the further.That the direct sum and the direct product of p-injective semimodules were still p-injective semimedules was proved.Moreover,the relationship between p-injective semimodules and divisible semimodules was analyzed in the case of the division semirings.Finally,it proved that non-zero p-injective semimodules exists over arbitrary proper semirings in that the conditions of p-injective semimodules＇notions are weaker than that of injective semimodules.
出处
《南昌大学学报（理科版）》
CAS
北大核心
2011年第2期111-114,共4页
Journal of Nanchang University(Natural Science)
基金
江西省自然科学基金资助项目(0611051)
关键词
p-内射半模
主理想
短正合列
真短正合列
p-injective semimodule
principal ideals
short exact sequence
short proper exact sequence
