Uniqueness of generators of principal ideals in rings of continuous functions
Uniqueness of generators of principal ideals in rings of continuous functions
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a upper R"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mi>R</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">aR</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the principal right ideal generated in a ring <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by an element <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a"> <mml:semantics> <mml:mi>a</mml:mi> …