Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T19:56:09.693Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on commutative Baer rings III

Published online by Cambridge University Press:  09 April 2009

T. P. Speed
T. P. Speed
Affiliation:
Department of Probability and Statistics The University SheffieldS10 30DU. K.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If R is a commutative semiprime ring with identity Kist [4], [5] has shown that R can be embedded into a commutative Baer ring B(R), and has given some properties of this embedding. More recently Mewborn [7] has given a construction which embeds R into a commutative Baer ring with the stronger property that every annihilator is generated by an idempotent. Both of these constructions involve a representation of R as a ring of global sections of a sheaf over a Boolean space.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 1 , February 1973 , pp. 15 - 21
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Amemiya, I., ‘A general spectral theory in semi-ordered linear spaces’, J. Fac. Sci. Hokk. Univ. 12 (1953), 111–156.Google Scholar
[2]Bernau, S. J., ‘Orthocompletions of lattice groups’, Proc. Lond. Math. Soc. 16 (1966), 107–30.CrossRefGoogle Scholar
[3]Conrad, P. F., ‘The lateral completion of a lattice-ordered group’, Proc. Lond. Math. Soc. 19 (1969), 444–480.CrossRefGoogle Scholar
[4]Kist, J., ‘Minimal prime ideals in commutative semigroups’, Proc. Lond. Math. Soc. 13 (1963), 31–50.CrossRefGoogle Scholar
[5]Kist, J., ‘Compact spaces of minimal prime ideals’, Math. Z. 111 (1969), 151–158.CrossRefGoogle Scholar
[6]Lambek, J., Lectures on Rings and Modules (Blaisdell 1966).Google Scholar
[7]Mewborn, A. C., ‘Regular rings and Baer rings’ (to appear).Google Scholar
[8]Sikorski, R., Boolean Algebras (Springer (1964)).Google Scholar
[9]Speed, T. P. and Evans, M. W., ‘A note on commutative Baer rings’, J. Aust. Math. Soc. 13 (1971), 1–6.CrossRefGoogle Scholar
[10]Speed, T. P., ‘A note on commutative Baer rings II’, J. Aust. Math. Soc. 14 (1972), 257–263.CrossRefGoogle Scholar