Coherence of power series rings over pseudo-Bezout domains
نویسندگان
چکیده
منابع مشابه
Power Series over Generalized Krull Domains
We resolve an open problem in commutative algebra and Field Arithmetic, posed by Jarden – Let R be a generalized Krull domain. Is the ring R[[X]] of formal power series over R a generalized Krull domain? We show that the answer is negative.
متن کاملAutomorphisms of Formal Power Series Rings over a Valuation Ring
The aim of this paper is to report on recent work on liftings of groups of au-tomorphisms of a formal power series ring over a eld k of characteristic p to characteristic 0, where they are realised as groups of automorphisms of a formal power series ring over a suitable valuation ring R dominating the Witt vectors W(k): We show that the lifting requirement for a group of automorphisms places se...
متن کاملON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS
Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse ske...
متن کاملAnti-archimedean Rings and Power Series Rings
We define an integral domain D to be anti-Archimedean if ⋂∞ n=1 a nD 6= 0 for each 0 6= a ∈ D. For example, a valuation domain or SFT Prüfer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show that D is anti-Archimedean ⇔ D[[X1, . . .
متن کاملFormal power series rings, inverse limits, and I-adic completions of rings Formal semigroup rings and formal power series rings
We next want to construct a much larger ring in which infinite sums of multiples of elements of S are allowed. In order to insure that multiplication is well-defined, from now on we assume that S has the following additional property: (#) For all s ∈ S, {(s1, s2) ∈ S × S : s1s2 = s} is finite. Thus, each element of S has only finitely many factorizations as a product of two elements. For exampl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90085-8