半群环的主理想升链条件问题  

Problem of Ascending Chain Condition for Principal Ideal of Semigroup Rings

作　　者：马晨江[1] 

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《三峡大学学报（自然科学版）》2005年第1期91-92,共2页Journal of China Three Gorges University：Natural Sciences

摘　　要：在环为整环、半群为交换无挠可消摹群的条件下对半群环的主理想升链条件进行了研究.得 到了半群环满足“主理想升链条件”的必要条件,以及在U(S)={e}的条件下半群环满足“主理想 升链条件”的充要条件.The ascending chain condition for principal ideal(a.c.c.p.) of semigroup rings is discussed;under the condition that the rings are integral domains and the semigroups are commutative torsion-free and cancellative monoids.A necessary condition of a.c.c.p.of semigroup rings is obtained.And a necessary and sufficient condition of a.c.c.p.of semigroup rings is obtained under the condition U(S)={e}.

关 键 词：半群环 主理想 整环 充要条件 必要条件 交换 问题 链条 

分 类 号：O153[理学—数学] O152.7[理学—基础数学]