Let \((R, + ,\cdot)\) be a ring with \(1\) as the identity of \((R,\cdot)\) and \(0\) as the identity of \((R,+)\). Further, let \(a\in R\).
1 Please note that if \(R\) is commutative, every left zero divisor is also a right zero divisor.
2 Please note that this is equivalent to \(a\cdot b=0\Leftrightarrow a=0 \vee b=0\).
| | | | | created: 2014-08-31 13:20:40 | modified: 2019-06-29 08:50:48 | by: bookofproofs | references: 
 Modler, Florian; Kreh, Martin: “Tutorium Algebra”, Springer Spektrum, 2013