EXTENSIONS OF GENERALIZED α-RIGID RINGS

Authors : Lunqun OUYANG

Pages : 103-116

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Publication Date : 2008-06-01

Article Type : Research Paper

Abstract :For a ring endomorphism α, we introduce weak α-rigid and weak α-skew Armendariz rings which are a generalization of α-rigid rings, and investigated their properties. Moreover, we prove that a ring R is weak α-rigid if and only if for any n, the n by n upper triangular matrix ring Tninsert ignore into journalissuearticles values(R); is weak α-rigid. If R is semicommutative and weak α-rigid, it is proven that the ring R[x] and the ring insert ignore into journalissuearticles values(R[x]/insert ignore into journalissuearticles values(xn);); where insert ignore into journalissuearticles values(xn); is the ideal generated by xn and n is a positive integer, are weak α-skew Armendariz.
Keywords : weak α rigid, skew Armendariz ring, extension