Irreducible Divisor Graphs

Abstract

In Beck (1988), the author introduces the idea of a zero-divisor graph of a commutative ring. We generalize this idea to study factorization in integral domains and define irreducible divisor graphs. We use these irreducible divisor graphs to characterize certain classes of domains, including UFDs.

Keywords:

• Factorization
• Integral domain
• Irreducible divisor graph

Mathematics Subject Classification:

• 13A05
• 13G05
• 05C99

Notes

Communicated by A. Facchini.