Abstract
Let R be a commutative ring with unit. We study certain subrings R[X;Y,λ] of R[X][[Y]]=R[X1,…,Xn][[Y1,…,Ym]], where λ is a nonnegative real-valued increasing function. These subrings naturally arise from studying p-adic analytic variation of zeta functions over finite fields. In our previous work, we gave a necessary and sufficient condition for R[X;Y,λ] to be Noetherian when Y has more than one variable and λ grows as fast as linear. In this paper, we show that the same result holds even when Y has only one variable. This contradicts Davis and Wan's result stating that R[X;Y,λ] is always Noetherian if R is a field. We however found a mistake in their proof.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
