On Reduced archimedean skew power series rings

2020/09/03 by Hamed Mousavi, Mousavi, Hamed, Farzad Padashnik +3
Mathematics · #13F10 #13J05 #16P60 #16P70 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:13F10 #msc:13J05 #msc:16P60 #msc:16P70

paper · pdf · doi:10.48550/arxiv.2009.01473

7 pages

arxiv created 2020/09/03 · arxiv updated 2020/09/04

Abstract

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 α is a rigid automorphism of R, then the skew power series ring R[[x;α]] is right Archimedean reduced ring. We also provide some examples to justify the assumptions we made to obtain the required result.

Related

• Reduced Archimedean skew polynomial rings and skew power series rings
• The ascending chain condition for principal left or right ideals of skew generalized power series rings
• S-Noetherian generalized power series rings
• Skew polynomial rings over abelian and idempotent reflexive rings
• Left-App rings of skew generalized power series