We introduce the use of formal languages in place of zero-divisor graphs used to study theoretic properties of commutative rings. We show that a regular language called a graph language can be constructed from the set of zero-divisors of a commutative ring. We then prove that graph languages are equivalent to their associated graphs. We go on to define several properties of graph languages.
Joe A. Stickles, Jr, Department of Mathematics, Millikin University, Decatur, IL 62522 JStickles@mail.millikin.edu
Eades III, Harley D.
"Zero-Divisors and Their Graph Languages,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 10
, Article 4.
Available at: http://scholar.rose-hulman.edu/rhumj/vol10/iss2/4