query: Ring with additive group isomorphic to group of units
positive_passages.docid: 144442
positive_passages.text: Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?
negative_passages.docid: 127306
negative_passages.text: Is the group of units of a finite ring cyclic?
negative_passages.docid: 39576
negative_passages.text: Quotient ring being isomorphic to the initial ring
negative_passages.docid: 4353
negative_passages.text: Unit group of power series ring
negative_passages.docid: 84823
negative_passages.text: When is the group of units in $\mathbb{Z}_n$ cyclic?
negative_passages.docid: 148550
negative_passages.text: Units in quotient ring of $\mathbb Z[X]$
negative_passages.docid: 16023
negative_passages.text: Are associates unit multiples in a commutative ring with $1$?
negative_passages.docid: 89864
negative_passages.text: Units in finite polynomial rings
negative_passages.docid: 642
negative_passages.text: Does a surjective ring homomorphism have to be surjective on the unit groups?
negative_passages.docid: 10908
negative_passages.text: Associated elements in a ring
negative_passages.docid: 30236
negative_passages.text: isomorphic groups related in direct product.
negative_passages.docid: 148881
negative_passages.text: Aut(GxH) isomorphic to Aut(G)xAut(H)
negative_passages.docid: 38687
negative_passages.text: Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$
negative_passages.docid: 21840
negative_passages.text: Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
negative_passages.docid: 61491
negative_passages.text: Complex Ring Isomorphism
negative_passages.docid: 135701
negative_passages.text: An example of a group such that $G \cong G \times G$
negative_passages.docid: 158975
negative_passages.text: Isomorphism of centers of isomorphic groups