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Theoretical study demonstrates equivalent algebraic characterizations in G-Dedekind rings, highlighting structural links between regular modules and quotient rings.
In this paper, regular modules are introduced to characterize rings whose regular ideals are G -projective, called G -Dedekind rings, i.e., R is a G -Dedekind ring if and only if any regular R -module is a G -projective R -module; if and only if R / aR is a QF ring for any regular element a in R ; if and only if R is an r -Noetherian ring and every regular prime ideal (or every regular maximal ideal) of R is G -projective.
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Zhou et al. (2026) studied this question.
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