The categorical and algebraic aspects of near-modules and near-vector spaces

In this thesis we generalize some results from vector spaces to near-vector spaces in the sense of J. André. In particular, we establish the First Isomorphism Theorem, which leads us to proving that the category of near-vector spaces is an abelian category. We also include an algebraic proof of the non-trivial fact that a subspace of a near-vector space is itself a near-vector space. Other algebraic and categorical properties of near-vector spaces are also obtained.

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