Research Projects

Artinian rings, Noetherian rings of Krull dimension zero, are a central part of algebra and geometry. I. Beck introduced the concept of zero-divisor graphs associated to commutative rings in 1988. The proposed research aims to study graphs associated to Artinian rings, specifically Gorenstein Artinian rings. The study will focus on multilinear forms, zero-divisor graphs, and determining automorphism groups of these graphs. The goal is to understand the interplay between algebraic aspects and graph theoretic aspects.