Geodesic
Schreier and Hall varieties of unary algebras
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 24-28

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To every variety of unary algebras is put into correspondence a pair $(R,I)$, where $R$ is a monoid and $I$ is its left ideal satisfying the condition $\nu\lambda=\nu$ for all $\nu\in I$ and $\lambda\in R$. Properties of this pair are indicated which are equivalent to the original variety being a Schreier one (subalgebras of free algebras are free) or being a Hall variety (retracts of free algebras are free). 
@article{VMUMM_1983_3_a4,
     author = {L. A. Skornyakov},
     title = {Schreier and {Hall} varieties of unary algebras},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {24--28},
     publisher = {mathdoc},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a4/}
}
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L. A. Skornyakov. Schreier and Hall varieties of unary algebras. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 24-28. http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a4/