• A NOTE ON QUOTIENT FULL COMMUTATIVE NEAR-FIELD SPACES OVER A NEAR-FIELD (QF-C-NFS-NF)

Abstract

In this paper, We define a near-field space N to be an FL (full linear) near-field space if N is isomorphic to the full near-field space of linear transformations of a left sub near-field space over a division near-field space. N is QFL if its left maximal quotient near-field space is an FLnear-field space. In this paper we give necessary and sufficient conditions for a near-field space to be a QFL near-field space. We also generalize some results of Chase and Faith concerning sub-direct sum decompositions of near-field spaces whose left maximal quotient near-field space is the direct product of FL near-field spaces.