A Note on z-Ideals and z°-Ideals of the Formal Power Series Rings and Polynomial Rings in an Infinite Set of Indeterminates

• 作者: Ahmed Maatallah Ali Benhissi
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（3）
• 页码范围: 495-508
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386720000413

摘要

Let A be a ring.In this paper we generalize some results introduced by Aliabad and Mohamadian.We give a relation between the z-ideals of A and those of the formal power series rings in an infinite set of indeterminates over A.Consider A[[XA]]3 and its subrings A[[XΛ]]1,A[[XΛ]]2,and A[[XΛ]]α,where α is an infinite cardinal number.In fact,a z-ideal of the rings defined above is of the form I + (XΛ)i,where i =1,2,3 or an infinite cardinal number and I is a z-ideal of A.In addition,we prove that the same condition given by Aliabad and Mohamadian can be used to get a relation between the minimal prime ideals of the ring of the formal power series in an infinite set of indeterminates and those of the ring of coefficients.As a natural result,we get a relation between the z°-ideals of the formal power series ring in an infinite set of indeterminates and those of the ring of coefficients.