Ike Humminspurts
New member
A Boolean ring R is one in which x^2 = x for all x (elements in R).
(a) Prove that in a Boolean ring, every element is its own additive inverse. (Hint: Square a convenient element of R.)
(b) Prove that every Boolean ring is commutative. (Hint: Square another convenient element of R. You may want to eventually use part (a).)
(c) Prove that every non-trivial (i.e., not {0}) Boolean ring has characteristic 2.
Any help appreciated!
Thanks!
(a) Prove that in a Boolean ring, every element is its own additive inverse. (Hint: Square a convenient element of R.)
(b) Prove that every Boolean ring is commutative. (Hint: Square another convenient element of R. You may want to eventually use part (a).)
(c) Prove that every non-trivial (i.e., not {0}) Boolean ring has characteristic 2.
Any help appreciated!
Thanks!