Extending congruences on semigroups
Extending congruences on semigroups
The two main results are: (1) Let <italic>S</italic> be a semigroup which satisfies the relation <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a b c d equals a c b d"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mi>b</mml:mi> <mml:mi>c</mml:mi> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mi>a</mml:mi> <mml:mi>c</mml:mi> <mml:mi>b</mml:mi> <mml:mi>d</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">abcd = acbd</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, let <italic>A</italic> be …