The Journal of the Indian Mathematical Society

N. Raja Gop Ala Rao ¹

Affiliations
1 Andhra University, Waltair, A. P., IN

Abstract

In an earlier paper [4], we have introduced the notion of i?-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]).

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