Stably Free Modules over the Klein Bottle
Stably Free Modules over the Klein Bottle
Stably Free Modules over the Klein Bottle
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Introduction<br />
Constructing a <strong>Stably</strong> <strong>Free</strong> Module<br />
Applications to <strong>the</strong> <strong>Klein</strong> <strong>Bottle</strong><br />
Projective <strong>Modules</strong><br />
Definition - <strong>Stably</strong> <strong>Free</strong> Module<br />
An R-module P is stably free iff <strong>the</strong>re exists natural numbers m, n<br />
such that P ⊕ R m ∼ = R n .<br />
{<strong>Free</strong> <strong>Modules</strong>} ⊆ {<strong>Stably</strong> <strong>Free</strong> <strong>Modules</strong>} ⊆ {Projective <strong>Modules</strong>}<br />
Andrew Misseldine <strong>Stably</strong> <strong>Free</strong> <strong>Modules</strong> <strong>over</strong> <strong>the</strong> <strong>Klein</strong> <strong>Bottle</strong>