Prenormality of ideals and completeness of their quotient algebras
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TL;DRAbstract
It is well known that if a nontrivial ideal ℑ on κ is normal, its quotient Boolean algebra P(κ)/ℑ is $κ^+$-complete. It is also known that such completeness of the quotient does not characterize normality, since P(κ)/ℑ turns out to be $κ^+$-complete whene
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It is well known that if a nontrivial ideal ℑ on κ is normal, its quotient Boolean algebra P(κ)/ℑ is $κ^+$-complete. It is also known that such completeness of the quotient does not characterize normality, since P(κ)/ℑ turns out to be $κ^+$-complete whene
Keywords
QuotientMathematicsCompleteness (order theory)Quotient algebraIdeal (ethics)NormalityBoolean algebraAlgebra over a field
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