Around Zero-Divisor Graph of Skew Polynomial Rings over Real Matrix 2 by 2

Abstract

Abstract Let R be an associative ring with non-zero two-sided multiplicative identity. The zero-divisor of R, denoted by Z (R). The directed graph Γ(R) is a graph with vertices Z (R) − {0}, where x → y is an edge between distinct vertices x and y if and only if xy = 0. On the other hand, assume that σ is a ring endomorphism on R. The skew polynomial ring R[x; σ,] is the ring of polynomials (with indeterminate x) over R. In this paper, in the case that R = M 2(ℝ), we study the zero-divisor graph of the skew polynomial ring R[x;σ].