Abstract
A Boolean algebra B is a retract of a Boolean algebra A if there exist homomorphisms f and g mapping A and B into B and A, respectively, such that f ο g is the identity mapping on B. The condition implies that f is an epimorphism and g is a monomorphism, so that a retract of A may be simultaneously regarded as a quotient algebra and a subalgebra of A.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1974 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Halmos, P.R. (1974). Retracts. In: Lectures on Boolean Algebras. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9855-7_30
Download citation
DOI: https://doi.org/10.1007/978-1-4612-9855-7_30
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90094-0
Online ISBN: 978-1-4612-9855-7
eBook Packages: Springer Book Archive