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Published online by Cambridge University Press: 20 January 2009
The elements of the abstract number systems termed groups, rings, ideals, modules and algebras are mere symbols arranged in systems by means of consistent and independent postulates which isolate these systems from the complete realm of abstract mathematics. The postulates are usually chosen so as to generalise the special number systems which have been noticed in traditional mathematics and their independence and consistenc}" are usually proved by means of numerical examples. It is suggested in this note that the extents of the consistency and independence of a set of postulates should also be studied
page 49 note 1 CfBurnside, , Theory of groups (Cambridge 1897), p. 25.Google Scholar
page 49 note 2 CfBurnside, , op. cit., Chapter 6.Google Scholar
page 50 note 1 Ore, O., Trans. Amer. Math. Soc., 41 (1937), 266–275.Google Scholar
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