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Information Journal Paper

Title

A note on G-type rings

Pages

  71-78

Keywords

$G$-type ring 
$G$-type ideal 

Abstract

 In this article, we introduce and examine the concept of $G$-type rings. A ring $R$ is classified as a $G$-type ring if its total quotient ring, denoted by $Q$, is generated by a countable number of elements over $R$ as an $R$-algebra. Formally, $Q = R[S^{-1}]$, where $S$ is a countable set of regular elements in $R$. We establish that $R$ is $G$-type if and only if there exists a countable set of regular elements, denoted as $S$, such that every prime ideal disjoint from $S$ consists solely of zero-divisors.It is shown thatwhenever a ring $T$ is countably generated over a subring $R$, asan $R$-algebra, and $T$ is strongly algebraic over $R$, then $R$is $G$-type if and only if $T$ is $G$-type.

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