Rings whose cyclic modules are injective or projective
Rings whose cyclic modules are injective or projective
The object of this paper is to prove <bold>Theorem</bold>. <italic>For a ring</italic> <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> <italic>the following are equivalent</italic>: (i) <italic>Every cyclic right</italic> <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>-<italic>module is injective or projective</italic>. …