query: Show if an integral domain D satisfies DCC (descending chain condition), it must satisfy ACC (ascending chain condition).
positive_passages.docid: 23242
positive_passages.text: Commutative integral domain with d.c.c. is a field
negative_passages.docid: 3037
negative_passages.text: Integral domain without unity has prime characteristic?
negative_passages.docid: 92360
negative_passages.text: Every principal ideal domain satisfies ACCP.
negative_passages.docid: 13147
negative_passages.text: Proof verification - Minimal polynomial of $\alpha$ has integer coef.s iff its an alg. integer
negative_passages.docid: 83871
negative_passages.text: GCDs in integral domains are unique up to unit factors (associates)
negative_passages.docid: 118809
negative_passages.text: If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
negative_passages.docid: 151018
negative_passages.text: Proving that any finite integral domain is a field.
negative_passages.docid: 107057
negative_passages.text: How to show that any separable space is CCC
negative_passages.docid: 17161
negative_passages.text: Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous?
negative_passages.docid: 78950
negative_passages.text: Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
negative_passages.docid: 93118
negative_passages.text: How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
negative_passages.docid: 141078
negative_passages.text: Domain over which a polynomial is strictly positive
negative_passages.docid: 44653
negative_passages.text: $(\int f_1d\mu)^2+\cdots+(\int f_nd\mu)^2\leq(\int \sqrt{f_1^2+\cdots+f_n^2}d\mu)^2$
negative_passages.docid: 147722
negative_passages.text: Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?
negative_passages.docid: 150011
negative_passages.text: Proof completeness of $(X,d)$ given $d$ is French railway metric
negative_passages.docid: 120292
negative_passages.text: How to formally prove: if $d\mid da+b$, then $d\mid b$?
negative_passages.docid: 100303
negative_passages.text: A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules