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XV.—On Non-Associative Combinations

  • I. M. H. Etherington (a1)

Numerous combinatory problems arise in connection with a set of elements subject to a non-associative process of composition—let us say of multiplication—commutative or non-commutative.

Non-associative products may be classified according to their shape. By the shape of a product I mean the manner of association of its factors without regard to their identity. Shapes will be called commutative or non-commutative according to the type of multiplication under consideration. Thus if multiplication is non-commutative, the products (AB.C)D and (BA.C)D are distinct but have the same shape, while D(AB.C) has a different shape. The three expressions, however, have the same commutative shape. I confine attention to products (like these) in which the factors are combined only two at a time.

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Proceedings of the Royal Society of Edinburgh
  • ISSN: 0370-1646
  • EISSN: 2059-9153
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh
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