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The Extended Center of Coproducts

Published online by Cambridge University Press:  20 November 2018

Wallace S. Martindale 3rd
Wallace S. Martindale 3rd*
Affiliation:
University of Massachusetts, Amherst, Ma 01003
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Abstract

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The sole purpose of this paper is to prove that if R1 and R2 are algebras with 1 over a common field F, with each (Ri:F) > 1 and at least one (Ri:F) > 2, then the extended center of the coproduct R1∐R2 is equal to F.

Keywords

16A1216A08coproductextended center
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 2 , 01 June 1982 , pp. 245 - 248
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Bergman, G., Modules over coproducts of rings, Trans. Amer. Math. Soc. 200 (1974), 1-32.Google Scholar
2. Lichtman, A. I., The primitivity of free products of associative algebras, J. Algebra 54 (1978), 153-158.Google Scholar
3. Martindale, W. S., 3rd, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576-584.Google Scholar
4. Martindale, W. S., 3rd and M. S.Montgomery, The normal closure of coproducts of domains, submitted for publication.Google Scholar