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Embedding semirings in semirings with multiplicative unit

Published online by Cambridge University Press:  09 April 2009

K. R. Pearson
Affiliation:
University of AdelaideSouth Australia
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A topological semiring is a system (S, +, ·) where (S, +) and (S, ·) are topological semigroups and · distributes across + as in a ring; that is, for all x, y, z in S, The operations + and · are called addition and multiplication respectively.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Bourbaki, N., Topologie générale (Actualités scientifiques et industrielles no. 1142, 1961).Google Scholar
[2]Hewitt, E., ‘Compact monothetic semigroups’, Duke Math. J. 23 (1956), 447457.CrossRefGoogle Scholar
[3]Hewitt, E. and Ross, K. A., Abstract harmonic analysis, Vol. 1 (Springer-Verlag, Berlin, 1963).Google Scholar
[4]Kurosh, A. G.Lectures on general algebra (Chelsea, New York, 1963).Google Scholar
[5]Miranda, A. B. Paalman-de, Topological semigroups (Mathematisch Centrum, Amsterdam, 1964).Google Scholar
[6]Selden, J., Theorems on topological semigroups and semirings (Doctoral Dissertation, University of Georgia, 1963).Google Scholar
[7]Selden, J., ‘A note on compact semiringsProc. Amer. Math. Soc. 17 (1966), 882886.Google Scholar
[8]Wallace, A. D., ‘The structure of topological semigroups’, Bull. Amer. Math. Soc. 61 (1955), 95112.CrossRefGoogle Scholar
[9]Zassenhaus, H., The theory of groups (2nd ed., Chelsea, New York, 1958).Google Scholar