Geodesic
Almost primitive elements of free nonassociative (anty)commutative algebras of small rank
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 19-24

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Criteria for homogeneous elements to be almost primitive are obtained and algorithms to recognize homogeneous almost primitive elements are constructed for free nonassociative commutative and anticommutative algebras of rank $1$ and $2$. 
@article{VMUMM_2012_5_a3,
     author = {A. V. Klimakov},
     title = {Almost primitive elements of free nonassociative (anty)commutative algebras of small rank},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {19--24},
     publisher = {mathdoc},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a3/}
}
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A. V. Klimakov. Almost primitive elements of free nonassociative (anty)commutative algebras of small rank. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 19-24. http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a3/