Abstract
For any ring R, let ℐ (R) be the unique Boolean lattice of two sided ideals which is isomorphic to the lattice of natural classes of non-singular right R-modules N f(R). Let 1 = 1 R = 1 Q ∈ R ⊂ Q be rings with R ⊂ Q an essential extension of right R-modules. Under some appropriate assumptions it is shown that there is an isomorphism of Boolean lattices Ψ: ℐ (R) → ℐ (Q). The natural inclusion map φ: R → Q, induces a natural order preserving map φ*: N f(Q → N f(R of the Boolean lattices of natural classes of Q and R. It is shown that φ* is essentially the inverse of Ψ.
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Dauns, J. (2010). Over Rings and Functors. In: Van Huynh, D., López-Permouth, S.R. (eds) Advances in Ring Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0286-0_9
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DOI: https://doi.org/10.1007/978-3-0346-0286-0_9
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