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Armendariz rings and gaussian rings [PDF]

Communications in Algebra, 1998
We prove a number of results concerning Armendariz rings and Gaussian rings. Recall that a (commutative) ring R is (Gaussian) Armendariz if for two polynomials f,g∈R[X] (the ideal of R generated by the coefficients of f g is the product of the ideals generated by the coefficients of f and g) fg = 0 implies a i b j=0 for each coefficient a i of f and b ...
VÍCTOR Camillo, D D Anderson
exaly   +4 more sources

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On Weak Armendariz Rings

Communications in Algebra, 2006
We introduce weak Armendariz rings which are a generalization of semicommutative rings and Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak Armendariz if and only if for any n, the n-by-n upper triangular matrix ring T n (R) is weak Armendariz.
Zhongkui Liu, Renyu Zhao
exaly   +2 more sources

On Skew Armendariz Rings

Communications in Algebra, 2003
Abstract For a ring endomorphism α, we introduce α-skew Armendariz rings which are a generalization of α-rigid rings and Armendariz rings, and investigate their properties. Moreover, we study on the relationship between the Baerness and p.p.-property of a ring R and these of the skew polynomial ring R[x; α] in case R is α-skew Armendariz.
Tai Keun Kwak, Chan Yong Hong
exaly   +2 more sources