کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595923 1336141 2015 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Noetherian property of subrings of power series rings II
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Noetherian property of subrings of power series rings II
چکیده انگلیسی

Let R   be a commutative ring with unit. We study certain subrings R[X;Y,λ]R[X;Y,λ] of R[X][[Y]]=R[X1,…,Xn][[Y1,…,Ym]]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]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]R[X;Y,λ] is always Noetherian if R is a field. We however found a mistake in their proof.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 219, Issue 9, September 2015, Pages 4055–4060
نویسندگان
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