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A note on commutative Baer rings III

Published online by Cambridge University Press:  09 April 2009

T. P. Speed
Affiliation:
Department of Probability and Statistics The University SheffieldS10 30DU. K.
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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
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), 111156.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), 444480.CrossRefGoogle Scholar
[4]Kist, J., ‘Minimal prime ideals in commutative semigroups’, Proc. Lond. Math. Soc. 13 (1963), 3150.CrossRefGoogle Scholar
[5]Kist, J., ‘Compact spaces of minimal prime ideals’, Math. Z. 111 (1969), 151158.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), 16.CrossRefGoogle Scholar
[10]Speed, T. P., ‘A note on commutative Baer rings II’, J. Aust. Math. Soc. 14 (1972), 257263.CrossRefGoogle Scholar