# Questions tagged [boolean-ring]

Use this tag for questions related to Boolean rings such as the ring of integers modulo 2.

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### Power Set of $X$ is a Ring with Symmetric Difference, and Intersection

I'm studying for an abstract algebra exam and one of the review questions was this: Let $X$ be a set, and $\mathcal P(X)$ be the power set of $X$. Consider the operations $\Delta$ = symmetric ...
GRE 9768 #60 on what appears to be Boolean rings: Ian Coley's approach is to prove $(I)$ and $(I) \implies (II) \implies (III)$ I think $(II) \implies (I)$. My attempt: $$(s+t)^2=s^2+t^2 \... 1answer 62 views ### Rings in which each element is a sum of n commuting idempotents Let n be a nonnegative integer. Let R be a nonunital ring such that every element of R is a sum of n pairwise commuting idempotents. (As usual, the class of nonunital rings includes the class ... 1answer 69 views ### GRE 9768 #60 Boolean non-commutative rings: Prove (-s)^2=s^2 without commutativity. GRE 9768 #60 Ian Coley's approach is to prove (I) and (I) \implies (II) \implies (III) In proving (I), how do we prove$$(-s)^2=s^2 without commutativity (but with $s=s^2$, if need ...
Let's say that f(x) is a function with its domain called $A$ with its codomain labeled $B$. The indicator function $I_{\{p\}}(x)$ has a value of the multiplicative identity, $1$, when $x=p$, and $0$ ...