On reduced archimedean skew power series rings

被引：1
|
作者：
Mousavi, Hamed [1 ]
Padashnik, Farzad [2 ]
Qureshi, Ayesha Asloob [3 ]
机构：
[1] Georgia Inst Technol, Math Dept, 686 Cherry St NW, Atlanta, GA 30313 USA
[2] Isfahan Univ, Fac Math Sci, Dept Pure Math, Esfahan, Iran
[3] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2022年 / 21卷 / 03期
关键词：
Skew power series ring; generalized power series rings; right (or left) Archimedean ring; annihilator; ascending chain conditions for principal one-sided ideals; ordered monoids; EXTENSIONS; ACCP; BAER;
D O I：
10.1142/S0219498822500426
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove that if R is an Archimedean reduced ring and satisfy ACC on annihilators, then R[[x]] is also an Archimedean reduced ring. More generally, we prove that if R is a right Archimedean ring satisfying the ACC on annihilators and alpha is a rigid automorphism of R, then the skew power series ring R[[x; alpha]] is right Archimedean reduced ring. We also provide some examples to justify the assumptions we made to obtain the required result.
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页数：9
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