All mathematicians accept the axioms of vector space. Of course, there are people out there who do not. Some people try to derive the existence of zero element from other axioms. However, we can prove that the existence axiom of zero element is independent of other axioms as all mathematicians would think so. Furthermore, we introduce an equivalence relation to make vector spaces from sets in partial absence of the vector space axioms. We shall show that this equivalence relation has a strange property, and we found that there is a connection between the way of our making vector spaces and the construction of the Grothendieck group.
ベクトル空間の公理系の一部を欠く集合の構成と同値関係によるベクトル空間化
ベクトル空間の公理系の一部を欠く集合の構成と同値関係によるベクトル空間化
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