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Boolean Algebra Retracts
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 339-344

Voir la notice de l'article provenant de la source Cambridge University Press

A Boolean algebra B is a retract of an algebra A if there exist homomorphisms ƒ: B → A and g: A → B such that gƒ is the identity map B. Some important properties of retracts of Boolean algebras are stated in [3, §§ 30, 31, 32]. If A and B are a-complete, and A is α-generated by B, Dwinger [1, p. 145, Theorem 2.4] proved necessary and sufficient conditions for the existence of an α-homomorphism g: A → B such that g is the identity map on B. Note that if a is not an infinite cardinal, B must be equal to A. The dual problem was treated by Wright [6]; he assumed that A and B are σ-algebras, and that g: A → B is a σ-homomorphism, and gave conditions for the existence of a homomorphism ƒ:B → A such that gƒ is the identity map. 
Cramer, Timothy. Boolean Algebra Retracts. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 339-344. doi: 10.4153/CJM-1971-034-3
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[1] 1. Dwinger, Ph., Retracts in Boolean algebras, Proc. Sympos. Pure Math., Vol. II, pp. 141–151 (Amer. Math. Soc, Providence, R. I., 1961). Google Scholar

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[6] 6. Wright, J. D. M., A lifting theorem for Boolean a-algebras, Math. Z. 112 (1969), 326–334. Google Scholar

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