Extending congruence relations
Extending congruence relations
If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper A"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">A</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper B"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">B</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {B}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are algebras, where <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper A …