Geodesic
About G-rings
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 13-18.

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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.
DOI : 10.14712/1213-7243.2015.196
Classification : 13D02, 13D05
Keywords: G-ring; pullback; trivial extension 
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Mahdou, Najib. About G-rings. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 13-18. doi : 10.14712/1213-7243.2015.196. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.196/

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