The Nikodym and Grothendieck properties of Boolean algebras and rings related to ideals

Damian Sobota, Tomasz Żuchowski

For an ideal $\mathcal{I}$ in a $\ddot{I}ƒ$-complete Boolean algebra $\mathcal{A}$, we show that if the Boolean algebra $\mathcal{A}⟨\mathcal{I}⟩$ generated by $\mathcal{I}$ d…