Chain Condition on Annihilators and Strongly Hopfian Property in Hurwitz Series Ring  

作　　者：All Benhissi 

机构地区：[1]Department of Mathematics, Faculty of Sciences University of Monastir, 5000 Monastir, Tunisia

出　　处：《Algebra Colloquium》2014年第4期635-646,共12页代数集刊（英文版）

摘　　要：In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.

关 键 词：Hurwitz series NILRADICAL ANNIHILATORS chain condition strongly Hopfian 

分 类 号：O153.3[理学—数学] O156.4[理学—基础数学]