Let $R$ be a commutative ring with $1$, $R[[x]]$ be the power series ring over $R$ and $A$ be an (prime) ideal of $R[[x]]$ with $xnotin A$ and ${f_i}_{i=1}^infty$ be a sequence of element of $A$. Now I have two questions:
Is $fmathrel{:=}f_1+xf_2+x^2f_3+dotsb+x^nf_{n+1}+dotsb$ a well defined element of $R[[x]]$?
(Since we can find the coefficient of $x^n$ in $f$ for each $n$, it seems that $f$ is well defined.)
If (1) is true is $fin A$? (If (1) is true and (2) is not true, under what conditions is (2) true?)
MathOverflow Asked on November 9, 2021
0 Answers1 Asked on January 19, 2021 by adittya-chaudhuri
cech cohomology ct category theory grothendieck topology nonabelian cohomology
0 Asked on January 17, 2021 by harry-gindi
0 Asked on January 17, 2021 by manfred-weis
1 Asked on January 16, 2021 by learning-math
geometric probability pr probability probability distributions st statistics
18 Asked on January 16, 2021
big list mathematics education open problems soft question thesis
3 Asked on January 16, 2021 by jochen-glueck
fa functional analysis linear algebra matrix analysis oa operator algebras operator theory
1 Asked on January 15, 2021
1 Asked on January 15, 2021 by no_idea
10 Asked on January 14, 2021 by edmund-harriss
big list ho history overview mathematical philosophy sociology of math
1 Asked on January 13, 2021 by david-jones
computational number theory conjectures nt number theory prime numbers
0 Asked on January 13, 2021 by jianrong-li
1 Asked on January 12, 2021
0 Asked on January 12, 2021 by francesco-polizzi
combinatorial group theory finite groups gap geometric group theory gr group theory
2 Asked on January 11, 2021 by user839372
ac commutative algebra coalgebras hopf algebras reference request
0 Asked on January 10, 2021 by goulifet
duality fa functional analysis integration schwartz distributions
0 Asked on January 10, 2021 by stabilo
cones derived categories modules quasi isomorphism triangles
0 Asked on January 9, 2021 by longyearbyen
0 Asked on January 9, 2021 by user164237
1 Asked on January 9, 2021 by bill-bradley
ca classical analysis and odes convex analysis convex optimization matrices permanent
1 Asked on January 9, 2021 by lrnv
Get help from others!
Recent Answers
Recent Questions
© 2022 AnswerBun.com. All rights reserved.