Basis and an Equibasis in a B-Vector Space

Abstract

In an earlier paper [4], we have introduced the notion of iβ-extension of an abelian group and also that of a R- vector space (B being a commutative regular ring with 1) (Definitions 1 and 2 of [4]), as generalisations to the concepts of Foster's Boolean extension of an abelian group [1] and Subrahmanyam's Boolean vector spaces [5] respectively, where we have shown, under a suitable definition of a basis (Definition 6 of [4]), that any vector space over a commutative regular ring with 1 admits a basis if and only if it is isomorphic with the 22-extension of a suitable abelian group (Theorem 7 of [4]).