Open AccessAround Zero-Divisor Graph of Skew Polynomial Rings over Real Matrix 2 by 2
Author(s) -
Amihood Amir
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1341/6/062022
Subject(s) - zero divisor , mathematics , combinatorics , multiplicative function , reduced ring , skew , discrete mathematics , graph , ring (chemistry) , polynomial ring , principal ideal ring , polynomial , physics , mathematical analysis , chemistry , organic chemistry , astronomy
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 ].