query: Is a field just a commutative ring?
positive_passages.docid: 10866
positive_passages.text: What is difference between a ring and a field?
negative_passages.docid: 11541
negative_passages.text: Examples of a non-commutative division ring
negative_passages.docid: 88307
negative_passages.text: Commutative property of ring addition
negative_passages.docid: 28688
negative_passages.text: why is a simple ring not semisimple?
negative_passages.docid: 75558
negative_passages.text: Counter-example for prime ideals in a non commutative ring.
negative_passages.docid: 98540
negative_passages.text: If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
negative_passages.docid: 77862
negative_passages.text: Question about fields and quotients of polynomial rings
negative_passages.docid: 112909
negative_passages.text: is a number field by definition a subfield of $ \mathbb C $?
negative_passages.docid: 139463
negative_passages.text: Commutative integral domain does not finitely generate its field of fractions
negative_passages.docid: 151794
negative_passages.text: Can an ideal in a commutative integral domain be its own square?
negative_passages.docid: 121643
negative_passages.text: Why isn't the zero ring the field with one element?
negative_passages.docid: 23242
negative_passages.text: Commutative integral domain with d.c.c. is a field
negative_passages.docid: 16643
negative_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 133878
negative_passages.text: Ring of order $p^2$ is commutative.
negative_passages.docid: 92962
negative_passages.text: Rings with $a^5=a$ are commutative
negative_passages.docid: 77854
negative_passages.text: Which cyclotomic fields are different?
negative_passages.docid: 23641
negative_passages.text: Quotient ring of field is zero or itself.