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- W1697333947 abstract "In this paper, we introduce a class of rings in which every nilpotent element is central. This class of rings generalizes so-called reduced rings. A ring $R$ is called {it central reduced} if every nilpotent element of $R$ is central. For a ring $R$, we prove that $R$ is central reduced if and only if $R[x_1,x_2,ldots,x_n]$ is central reduced if and only if $R[[x_1,x_2,ldots,x_n]]$ is central reduced if and only if $R[x_1,x_1^{-1},x_2,x_2^{-1},ldots,x_n,x_n^{-1}]$ is central reduced. Moreover, if $R$ is a central reduced ring, then the trivial extension $T(R,R)$ is central Armendariz." @default.
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- W1697333947 date "2013-12-14" @default.
- W1697333947 modified "2023-10-18" @default.
- W1697333947 title "Rings in which every nilpotent is central" @default.
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