Amalgamated Duplication of A Ring along An Ideal

Amalgamated Duplication of A Ring along An Ideal

邱曼菱(Men-Ling Chiu)

指導教授 ： 王心如

國立中正大學/理學院/數學系應用數學研究所/碩士(2013年)

摘要

假設R是一個交換環且I是一個理想
假設R × R的子環是由(r,r + i) for r ∈ R and i ∈ I 所組成的
引用一個新的稱為amalgamated duplication of a ring along an ideal
最後說明這些圖是屬於 二分圖,平面,或Km

並列摘要

Let R be a commutative ring with identity and let I be an ideal of R.
Let the subring of R × R consisting of the elements (r,r + i) for r ∈ R and i ∈ I.
Introduce a new general construction, called the amalgamated duplication
of a ring R along an R-module E. Then we illustrate these graphics as the bipartite,
planar and Km of the zero-divisor graph of the ring.

並列關鍵字

amalgamated

參考文獻

[1] R. Diestel, Graph Theory, Springer-Verlag, New Your, 1997.

[2] M. D'Anna, A construction of Gorenstein rings, J. Algebra 306 (2006) 509-519.

[3] M. D'Anna and M. Fontana, The amalgamated duplication of a ring along a multiplicative-canonical ideal, Ark. Mat., 45 (2007) 241-252

[4] M. D'Anna, M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, J. Algebra Appl. Vol. 6, No. 3 (2007) 443-459.

[5] H.R. Maimani, S. Yassemi, Zero-divisor graphs of amalgamated duplication of a ring along an ideal, J. Algebra 212 (2008) 168-174.