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A note on near-rings of mappings

  • Sadayuki Yamamuro (a1)

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Hanna Neumann was one of the pioneers of the algebraic theory of nearrings. In the functional analysis, the near-rings appear as the sets of non-linear mappings of a space into itself. The relations between the algebraic properties of these near-rings and the analytic structures of the spaces and mappings involved have not been fully investigated. The purpose of this note is to consider one of such problems.

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References

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[1]Bonic, R. and Frampton, J., ‘Smooth functions on Banach manifolds’, J. Math. Mec. 15 (1966), 877898.
[2]Eidelheit, M., ‘On isomorphisms of rings of linear operators’, Studia Math. 9 (1940), 97105.
[3]Magill, K. D. Jr, ‘Automorphisms of the semigroup of all differentiable functions’, Glasgow Math. J. 8 (1967), 6366.
[4]Rickart, C. E., ‘One-to-one mappings of rings and lattices’, Bull. Amer. Math. Soc. 54 (1968), 758764.
[5]Yamamuro, S., ‘A note on semigroups of mappings on Banch spaces’, J. Austral. Math. Soc. 9 (1969), 455464.
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A note on near-rings of mappings

  • Sadayuki Yamamuro (a1)

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