query: Isn't commutative property of $+$ in a ring obvious from other axioms?
positive_passages.docid: 150309
positive_passages.text: Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1?
negative_passages.docid: 109070
negative_passages.text: Question about the proof of the distributive property for sets
negative_passages.docid: 2709
negative_passages.text: How to show that every Boolean ring is commutative?
negative_passages.docid: 8787
negative_passages.text: In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
negative_passages.docid: 111104
negative_passages.text: Ring theory notation question
negative_passages.docid: 17895
negative_passages.text: Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
negative_passages.docid: 153291
negative_passages.text: Why a ring homomorphism from a local ring will not map a non-unit to a unit？
negative_passages.docid: 128813
negative_passages.text: Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
negative_passages.docid: 150320
negative_passages.text: Why does $a^{b}·a^{c}=a^{b+c}$?
negative_passages.docid: 38817
negative_passages.text: Why is the ring of matrices over a field simple?
negative_passages.docid: 125348
negative_passages.text: Does $\det(A + B) = \det(A) + \det(B)$ hold?
negative_passages.docid: 80088
negative_passages.text: What possible characteristics may a local commutative unital ring have?
negative_passages.docid: 72230
negative_passages.text: Equivalence of definitions of prime ideal in commutative ring
negative_passages.docid: 102316
negative_passages.text: why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
negative_passages.docid: 82609
negative_passages.text: Ring such that $x^4=x$ for all $x$ is commutative
negative_passages.docid: 130159
negative_passages.text: Meaning of ring notation $\Bbb Z_{(p)}$ in commutative algebra [localization]
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$