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A note on commutative Baer rings

Published online by Cambridge University Press:  09 April 2009

T. P. Speed
T. P. Speed
Affiliation:
Department of Probability & Statistics, The University Sheffield, S3 7RH, England
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In this note we study commutative Baer rings, uniting the abstract algebraic approach with the approach of [3] using minimal prime ideals. Some new characterisations of this class of rings are obtained, relations between the minimal prime ideals of a commutative Baer ring B and its algebra EB of idempotents are considered, and some results concerning the direct decomposition of commutative Baer rings are given. We then study Baer ideals, and finally state without proof a new construction of the Baer extension of a commutative semiprime ring.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 257 - 263
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Abian, A., ‘Direct Product Decomposition of Commutative Semisimple Rings’, Proc. Amer. Math. Soc. 24 (1970), 502–507.Google Scholar
[2]Gillman, L. and Jerison, M., Rings of Continuous Functions (Van Nostrand 1960.)CrossRefGoogle Scholar
[3]Kist, J., ‘Minimal Prime Ideals in Commutative Semigroups’, Proc. Lond. Math. Soc. Ser. 3, 13 (1963), 31–50.CrossRefGoogle Scholar
[4]Speed, T. P., ‘A Note on Stone Lattices’, Can. Math. Bull. 14 (1971) 81–86.CrossRefGoogle Scholar