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Algebraically Closed Regular Rings

Published online by Cambridge University Press:  20 November 2018

Andrew B. Carson
Andrew B. Carson*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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In this paper all rings are commutative and have a unity. All ring homomorphisms preserve the unity. We let L denote the standard language for rings with two distinct constants, 0 and 1, playing the role of the zero and the unity respectively. A ring is regular if it satisfies the axiom (∀r) (∃r′)(rr′r = r) and it is algebraically closed if, for each integer n ≧ 1, it satisfies the sentence

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1036 - 1049
Copyright
Copyright © Canadian Mathematical Society 1974

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