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 ].

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