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A localic approach to minimal prime spectra

Published online by Cambridge University Press:  24 October 2008

Sun Shu-Hao
Affiliation:
Department of Mathematics, Sichuan University, P.R., China

Extract

Throughout this paper, A will denote a distributive lattice with 0 and 1; we shall write spec A for the prime spectrum of A (i.e. the set of prime ideals of A, with the Stone–Zariski topology), and max A, min A for the subspaces of spec A consisting of maximal and minimal prime ideals respectively. These two subspaces have rather different topological properties: max A is always compact, but not always Hausdorff (indeed, any compact T1-space can occur as max A for some A), and min A is always Hausdorff (in fact zero-dimensional), but not always compact. (For more information on max A and min A, see Simmons[3].)

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Johnstone, P. T.. Stone Spaces. Cambridge Studies in Advanced Math. no. 3 (Cambridge University Press, 1982).Google Scholar
[2]Johnstone, P. T.. Almost maximal ideals. Fund. Math. 123 (1984), 197207.CrossRefGoogle Scholar
[3]Simmons, H.. Reticulated rings. J. Algebra 66 (1980), 169192.CrossRefGoogle Scholar