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Inversive semirings

Published online by Cambridge University Press:  09 April 2009

Paul H. Karvellas
Paul H. Karvellas
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Canada
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A semiring (S, +,·) is a nonempty set S, endowed with associative operations of addition and multiplication, such that the multiplicative semigroup (S, ·) distributes over the addition. That is: x(y +z) = xy + xz and (x + y)z = xz + yz for all x, y and z in S. A topological semiring is a semiring, defined on a Hausdorff space, such that both of the operations are jointly continuous.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 3 , November 1974 , pp. 277 - 288
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Anzai, H., ‘On Compact Topological Rings’, Proc. Imp. Acad. Tokyo 19 (1943), 613–615.Google Scholar
[2]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, Vol. I (Amer. Math. Soc., 1961).Google Scholar
[3]Henriksen, M., ‘The an(a) = a Theoŕem for Semirings’, Math. Japon. 5 (1958), 21–24.Google Scholar
[4]Poinsignon Grillet, M. O., ‘Subdivision Rings of a Semiring’, Fund. Math. 67 (1970), 67–74.CrossRefGoogle Scholar
[5]Koch, R. J. and Wallace, A. D., ‘Notes on Inverse Semigroups’, Rev. Roum. de Math. Pures et Appl. 9 (1964), 1–6.Google Scholar
[6]La Torre, D. R., The Radical of a Semiring, Master's Thesis, The University of Tennessee, Knoxville (1962).Google Scholar
[7]Pearson, K. R., ‘Compact Semirings which are Multiplicatively Groups or Groups with Zero’, Math. Zeitschr. 106 (1968), 388–394.CrossRefGoogle Scholar
[8]Pearson, K. R., ‘The Three Kernels of a Compact Semiring’, J. Austral. Math. Soc. 10 (1969), 299–319.CrossRefGoogle Scholar
[9]Selden, J., ‘A Note on Compact Semirings’, Proc. Amer. Math. Soc. 15 (1964), 882–886.CrossRefGoogle Scholar
[10]Wallace, A. D., ‘The Structure of Topological Semigroups’, Bull. Amer. Math. Soc. 61 (1955), 95–112.CrossRefGoogle Scholar