The 𝐺𝐸₂ property for discrete subrings of 𝐶

The $GE_{2}$ property for discrete subrings of $\textbf {C}$
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by R. Keith Dennis PDF

Proc. Amer. Math. Soc. 50 (1975), 77-82 Request permission

The collection of discrete subrings of the complex numbers whose ${\text {SL} _2}$ is generated by elementary matrices is completely determined.

References

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A weakening of the Euclidean property for integral domains and applications to algebraic number theory

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