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 that whenever a ring $T$ is countably generated over a subring $R$, as an $R$-algebra, and $T$ is strongly algebraic over $R$, then $R$ is $G$-type if and only if $T$ is $G$-type.
Soltanpour, S. and Moslemi, B. (2024). A note on G-type rings. Journal of Advanced Mathematical Modeling, 14(3-English), 71-78. doi: 10.22055/jamm.2025.46283.2264
MLA
Soltanpour, S. , and Moslemi, B. . "A note on G-type rings", Journal of Advanced Mathematical Modeling, 14, 3-English, 2024, 71-78. doi: 10.22055/jamm.2025.46283.2264
HARVARD
Soltanpour, S., Moslemi, B. (2024). 'A note on G-type rings', Journal of Advanced Mathematical Modeling, 14(3-English), pp. 71-78. doi: 10.22055/jamm.2025.46283.2264
CHICAGO
S. Soltanpour and B. Moslemi, "A note on G-type rings," Journal of Advanced Mathematical Modeling, 14 3-English (2024): 71-78, doi: 10.22055/jamm.2025.46283.2264
VANCOUVER
Soltanpour, S., Moslemi, B. A note on G-type rings. Journal of Advanced Mathematical Modeling, 2024; 14(3-English): 71-78. doi: 10.22055/jamm.2025.46283.2264
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