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Keywords:
G-ring; pullback; trivial extension
G-ring; pullback; trivial extension
Summary:
In this paper, we are concerned with G-rings. We generalize the Kaplansky's theorem to rings with zero-divisors. Also, we assert that if $R \subseteq T$ is a ring extension such that $mT\subseteq R$ for some regular element $m$ of $T$, then $T$ is a G-ring if and only if so is $R$. Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.
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