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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2022.9
- 수록면
- 437 - 453 (17page)
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Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ∼ on S defined by letting a ∼ b if and only if annS(a) = annS(b), is an equivalence relation. The compressed zero-divisor graph ΓE(S) of S is the undirected graph whose vertices are the equivalence classes in duced by ∼ on S other than [0]S and [1]S, in which two distinct vertices [a]S and [b]S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R0[x] and the near-ring of the power series R0[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam.
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