query: If $R$ is commutative, the left $R-$module can be given the structure of right $R-$module.
positive_passages.docid: 147157
positive_passages.text: Modules over commutative rings
negative_passages.docid: 126295
negative_passages.text: What is an $R$-algebra?
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 137011
negative_passages.text: showing $\psi: R\to \mathbb C$ is ring isomorphism.
negative_passages.docid: 4790
negative_passages.text: Generators of a finitely generated free module over a commutative ring
negative_passages.docid: 43990
negative_passages.text: R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
negative_passages.docid: 156910
negative_passages.text: Necessary and sufficient condition for $R/IJ \cong R/I \times R/J$
negative_passages.docid: 69160
negative_passages.text: Show that the functor that takes $R$ to the set of invertible elements of $R[X]/(X^2-a)$ is representable.
negative_passages.docid: 79535
negative_passages.text: Prove that $R$ is a commutative ring if $x^3=x$
negative_passages.docid: 5893
negative_passages.text: On the commutative property of multiplication (domain of integers, possibly reals)
negative_passages.docid: 18971
negative_passages.text: Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
negative_passages.docid: 133706
negative_passages.text: If R is a local ring, then its maximal left-ideal is a left and right ideal
negative_passages.docid: 108601
negative_passages.text: Show structure of a commutative ring in a tensor product
negative_passages.docid: 8417
negative_passages.text: Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
negative_passages.docid: 153508
negative_passages.text: Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.
negative_passages.docid: 127044
negative_passages.text: Prove that a finitely-generated free module has a finite basis
negative_passages.docid: 50212
negative_passages.text: $R/Ra$ is an injective module over itself