Source: wikibot/proofs-of-elementary-ring-properties
= Proofs of elementary ring properties
{wiki=Proofs_of_elementary_ring_properties}
In abstract algebra, especially in the study of ring theory, various properties of rings can be proven using fundamental definitions and theorems. Here’s a brief overview of several elementary properties of rings along with proofs for each. \#\#\# 1. **Ring Non-emptiness** **Property:** Every ring \\( R \\) (with unity) contains the additive identity, denoted as \\( 0 \\).