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In Proposition 1.1 of [Math. Proc. Cambridge Phil. Soc. 64 (1968), No. 2, 251-264], P.M. Cohn famously claimed (without proof) that a commutative domain is atomic if and only if it satisfies the ...

Let $H$ be a commutative monoid (written multiplicatively). We say that a set $I \subseteq H$ is an ideal of $H$ if $IH = I$. The set $\mathcal I(H)$ of all ideals of $H$ is made into a (commutative) ...

I have been reading the following paper: https://www.sciencedirect.com/science/article/pii/S002240491000263X Proposition 2.4(ii) shows that if $\mathfrak D$ is a ring of $k$-linear differential ...

By an arithmetical ring is understood a commutative ring $R$ with identity for which the ideals form a distributive lattice, i.e., for which $(I+J)\cap K=(I\cap K)+(J\cap K)$ for all ideals $I, J$ ...