User talk:Randrjwr

The page, "Idempotents (Ring Theory)" either has an inconsistency or I am missing something. The second paragraph says: "In Boolean algebra, the main objects of study are rings in which all elements are idempotent under both addition and multiplication." Then, under the heading "Rings characterized by idempotents" it is stated "A ring in which all elements are idempotent is called a Boolean ring. Some authors use the term "idempotent ring" for this type of ring. In such a ring, multiplication is commutative and every element is its own additive inverse." If an element, say E, of a ring is idempotent under addition, then we must have E+E=E. But, if every element is its own additive inverse, then we have E+E=0. As I understand Boolean algebra, the latter is true, the former is not.

Am I missing something, or should this page be edited to remove the "idempotent under....addition" statement?

Randrjwr (talk) 00:20, 31 October 2017 (UTC)