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The McCoy condition on skew Poincaré-Birkhoff-Witt extensions. (English) Zbl 1479.16035

Let \(B\) be an associative ring with unity. \(B\) is called a (linearly) right McCoy ring, if the equality \(f(x)g(x) = 0\), where \(f(x), g(x)\) are (linear) polynomials in \(B\left[x\right] \setminus \left\{0\right\}\), implies that there exists a nonzero element \(c \in B\), such that \(f(x)c = 0\). Left McCoy rings are defined similarly. In this paper, the authors studied the notion of McCoy ring over the class of non-commutative rings of polynomial type known as skew Poincaré-Birkhoff-Witt extensions (also known as \(\sigma \)- PBW extensions), which is more general than iterated Ore extensions. As a consequence, they generalized several results about this notion considered in the literature for commutative rings and Ore extensions.

MSC:

16U80 Generalizations of commutativity (associative rings and algebras)
16S36 Ordinary and skew polynomial rings and semigroup rings
16S38 Rings arising from noncommutative algebraic geometry
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