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Characters of Cartesian Products of Algebras

Published online by Cambridge University Press:  20 November 2018

Seth Warner
Seth Warner*
Affiliation:
Duke University Durham, North Carolina
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Let R be a commutative ring with identity 1. A character of an R-algebra E is a homomorphism from E onto R, regarded as an algebra over itself. If (Eα) is a family of R-algebras indexed by a set A and if

then for every β ∈ A and every character vβ of Eβ, vβ o prβ is a character of E where prβ is the projection homomorphism from E onto Eβ. Further if A is finite and if the only idempotents of R are 0 and 1 (equivalently, if R is not the direct sum of two proper ideals), it is easy to see that every character of E is of this form.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 70 - 79
Copyright
Copyright © Canadian Mathematical Society 1959

References

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