An ideal-based zero-divisor graph of 2-primal near-rings
1
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact T_1-subspace. We also study the zero-divisor graph Γ_(I) (R) with respect to the completely semiprime ideal I of N. We show that Γ_(P)(R), where P is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph Γ_(P)(R).
Abstract
In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact T_1-subspace. We also study the zero-divisor graph Γ_(I) (R) with respect to the completely semiprime ideal I of N. We show that Γ_(P)(R), where P is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph Γ_(P)(R).
참고문헌 (12)
- D. D. Anderson, "Beck’s coloring of a commutative ring", J. Algebra, 159(2), pp.500~514 (1993)
- D. F. Anderson, "The zero-divisor graph of a commutative ring", J. Algebra, 217(2), pp.434~447 (1999)
- I. Beck, "Coloring of commutative rings", J. Algebra, 116(1), pp.208~226 (1988)
- J. A. Bondy, "Graph Theory with Applications" (1976), American Elsevier Publishing Co
- P. Dheena, "On strong IFP near-ring", ~
- R. Engelking, "General Topology" (1989), Heldermann Verlag
- J. R. Munkres, "Topology" (2005), Prentice-Hall of Indin
- G. Pilz, "Near-Rings" (1983), North-Holland
- S. P. Redmond, "An ideal-based zero-divisor graph of a commutative ring", Comm. Algebra, 31(9), pp.4425~4443 (2003)
- K. Samei, "On summand ideals in commutative reduced rings", Comm. Algebra, 32(3), pp.1061~1068 (2004)
- K. Samei, "The zero-divisor graph of a reduced ring", J. Pure Appl. Algebra, 209(3), pp.813~821 (2007)
- S. H. Sun, "Noncommutative rings in which every prime ideal is contained in a unique maximal ideal", J. Pure Appl. Algebra, 76(2), pp.179~192 (1991)