p-内射半模  

p-Injective semimodules

作　　者：黄福生[1] 杨俊燕[1] 余安安[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《南昌大学学报（理科版）》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)

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.

关 键 词：p-内射半模 主理想 短正合列 真短正合列 

分 类 号：O153.3[理学—数学]