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Abstracts from the 58^th European Society of Human Genetics (ESHG) Conference: Hybrid Posters. [PDF]

Eur J Hum Genet
europepmc   +1 more source

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 ...
Victor P. Camillo, D D Anderson
exaly   +3 more sources

Nilpotent Elements and Armendariz Rings

Journal of Algebra, 2008
Let \(R\) denote an associative ring with \(1\), and let \(\text{nil}(R)\) denote the set of nilpotent elements. Further, let \(f(x)=\sum_{i=0}^ma_ix^i,g(x)=\sum_{j=0}^nb_jx^j\in R[x]\) denote two arbitrary polynomials. One says that \(R\) is an Armendariz ring if \(f(x)g(x)=0\) implies that \(a_ib_j=0\) for all \(i\) and \(j\).
Ramon Antoine
exaly   +2 more sources

Armendariz Rings and Reduced Rings

Journal of Algebra, 2000
According to \textit{D. D. Anderson} and \textit{V. Camillo} [Commun. Algebra 26, No. 7, 2265-2272 (1998; Zbl 0915.13001)], a ring \(R\) is called Armendariz if whenever polynomials \(f(x)=a_0+a_1x+\cdots+a_m x^m\) and \(g(x)=b_0+b_1x+\cdots+b_nx^n\) in \(R[x]\) satisfy \(f(x)g(x)=0\), then \(a_ib_j=0\) for each \(i\), \(j\). It is shown that if a ring
Kim, Nam Kyun, Lee, Yang
exaly   +3 more sources

Armendariz and Reduced Rings

Communications in Algebra, 2004
Abstract A ring R is called Armendariz if, whenever in R[x], a i b j  = 0 for all i and j. In this paper, some “relatively maximal” Armendariz subrings of matrix rings are identified, and a necessary and sufficient condition for a trivial extension to be Armendariz is obtained. Consequently, new families of Armendariz rings are presented.
Tsiu-Kwen Lee, Yiqiang Zhou
exaly   +2 more sources