query: Direct sum of group rings
positive_passages.docid: 157840
positive_passages.text: Is it true that $(R\times S)[G]\cong R[G]\times S[G]$?
negative_passages.docid: 21466
negative_passages.text: $P$ is projective . Show that $P$ is a direct summand of a free $R-$ module
negative_passages.docid: 4353
negative_passages.text: Unit group of power series ring
negative_passages.docid: 93169
negative_passages.text: Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
negative_passages.docid: 42096
negative_passages.text: Direct product of Sylow subgroups
negative_passages.docid: 16476
negative_passages.text: Order of the product of two commuting elements with coprime orders in a group.
negative_passages.docid: 158873
negative_passages.text: Is every group the unit group of some ring?
negative_passages.docid: 138383
negative_passages.text: group of units in a topological ring
negative_passages.docid: 30236
negative_passages.text: isomorphic groups related in direct product.
negative_passages.docid: 66806
negative_passages.text: A nonsplit short exact sequence of abelian groups with $B \cong A \oplus C$
negative_passages.docid: 18361
negative_passages.text: Does the unit generate the additive group in a unital ring with cyclic additive group?
negative_passages.docid: 102971
negative_passages.text: Product of all elements of a finite group with an unique element of order 2
negative_passages.docid: 98155
negative_passages.text: Free products of cyclic groups
negative_passages.docid: 147298
negative_passages.text: How to find all subgroups of a direct product?
negative_passages.docid: 68128
negative_passages.text: Two term free resolution of an abelian group.
negative_passages.docid: 23077
negative_passages.text: Prove that the dihedral group $D_4$ can not be written as a direct product of two groups
negative_passages.docid: 64484
negative_passages.text: Left ideal $I$ is a direct summand of $R$ iff $I = Rr$, $r^2 = r$