极大p-内射半模和极大k-p-平坦半模  

Maximal p-Injective Semimodules and Maximal k-p-Flat Semimodules

作　　者：陆二伟 储茂权[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《南通大学学报（自然科学版）》2015年第4期75-82,共8页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(10971099)

摘　　要：若对半环L的每个极大主理想P及任意左L-半模同态f:P→M,总存在L-半模同态g:L→M,使得g|_p=f,则称左L-半模M为极大p-内射半模,若对半环L的任意极大左主理想P,同态列0→MP→I_Mi_pML是真正合列且I_Mi_P是k-正则(即I_Mi_P是单同态)的,则称右L-半模M为极大k-p-平坦半模.文章主要探究了极大p-内射半模与极大k-p-平坦半模的若干基本性质,并且研究了极大p-内射半模与极大k-p-平坦半模之间的关系.主要结果有:1)设{M_i}_(i∈l)是极大p-内射半模,则_(i∈I)M_i为极大p-内射半模当且仅当M_i为极大p-内射半模;2)若右L-半模M的每个有限生成子半模都是极大k-p-平坦半模,则M为极大k-p-平坦半模:3)设L,S为半环,E为左S-内射半模,M∈_sM_L,且M为极大k-p-平坦右L-半模,则Hom(M,E)为极大p-内射左L-半模.If P is a maximal main ideal of semiring L and f ： P → M is a left L-semimodule homomorphism, there is always a L-semimodule homomorphism g ： L→ M, satisfying g I p = f, then M is called maximal p-injective semi-module. If P is a maximal main ideal of semiring L and homomorphism sequence 0 → is a real exact sequence and IM , then M is called maximal k-p-flat semimodule. Somebasic properties of p-injective semimodule and k-p-flat semimodule were investigated, and the relationships of maxi- mal p-injective semimodule, maximal k-p-fiat semimodule, and the following results were obtained： 1）If {Mi} are maximal p-injective semimodules, then every M~ is a maximal p-injective semimodule. 2）If every finitely generated subsemimodule of right L-semimodule M is a maximal k-p-fiat semimodule, then M is a maximal k-p-fiat semimod- ule. 3）If L, S are semirings and E is a left S-injective semimodule, satisfying M E sML, and M is a maximal k-p-fiat right L-semimodule, then Horn（M, E） is a maximal p-injective left L-semimodule.

关 键 词：半模 极大p-内射半模 极大k-p-平坦半模 

分 类 号：O153.3[理学—数学]