Geodesic
Free algebras of variety of unars with Malcev's operation $p$, define by identity $p(x,y,x)=y$
Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 127-134.

Voir la notice de l'article provenant de la source Math-Net.Ru

In article is given construction of free algebras of the variety of algebras with one unary and one ternary Mal'cev's operation $p$, provided that operations is commute, defined by identity $p(x,y,x)=y$. It is proved decidability of word problem in free algebras and uniqueness of free basis. It is proved realization of Hopf property for free algebras of finitely rank. 
@article{CHEB_2011_12_2_a15,
     author = {V. L. Usol'cev},
     title = {Free algebras of variety of unars with {Malcev's} operation $p$, define by identity $p(x,y,x)=y$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {127--134},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a15/}
}
TY  - JOUR
AU  - V. L. Usol'cev
TI  - Free algebras of variety of unars with Malcev's operation $p$, define by identity $p(x,y,x)=y$
JO  - Čebyševskij sbornik
PY  - 2011
SP  - 127
EP  - 134
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a15/
LA  - ru
ID  - CHEB_2011_12_2_a15
ER  - 
%0 Journal Article
%A V. L. Usol'cev
%T Free algebras of variety of unars with Malcev's operation $p$, define by identity $p(x,y,x)=y$
%J Čebyševskij sbornik
%D 2011
%P 127-134
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a15/
%G ru
%F CHEB_2011_12_2_a15
V. L. Usol'cev. Free algebras of variety of unars with Malcev's operation $p$, define by identity $p(x,y,x)=y$. Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 127-134. http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a15/

[1] Freese R., McKenzie R., Commutator theory for congruence modular varieties, London, 1987

[2] Maltsev A. I., “K obschei teorii algebraicheskikh sistem”, Matem. sb., 35(77):1 (1954), 3–20

[3] Pixley A. F., “Distributivity and permutability of congruence relations in equational classes of algebras”, Proc. Amer. Math. Soc., 14:1 (1963), 105–109 | DOI | MR | Zbl

[4] Skornjakov L. A., “Unars”, Colloq. Math. Soc. J. Bolyai, 29, 1981, 735–743 | MR

[5] Kartashov V. K., “Kvazimnogoobraziya unarov”, Mat. zametki, 27:1 (1980), 7–20 | MR | Zbl

[6] Maltsev A. I., Algebraicheskie sistemy, Nauka, M., 1970 | MR

[7] Kilp M., Knauer U., Mikhalev A. V., Monoids, Acts and Categories with Applications to Wreath Products and Graphs, Walter de Gruyter, Berlin, 2000 | MR | Zbl

[8] Smirnov D. M., “O sootvetstvii mezhdu regulyarno opredelimymi mnogoobraziyami unarnykh algebr i polugruppami”, Algebra i logika, 17:4 (1978), 468–477 | MR | Zbl

[9] Kozhukhov I. B., “Polugruppy, nad kotorymi vse poligony rezidualno konechny”, Fund. i prikl. matematika, 4:4 (1998), 1335–1344 | MR | Zbl

[10] Kartashov V. K., “Ob unarakh s maltsevskoi operatsiei”, Universalnaya algebra i ee prilozheniya, Tez. dokl. mezhd. seminara, posv. pamyati prof. L. A. Skornyakova, Volgograd, 1999, 31–32

[11] Usoltsev V. L., “Svobodnye algebry mnogoobraziya unarov s maltsevskoi operatsiei, udovletvoryayuschei usloviyam Piksli”, Izvestiya vuzov. Matematika, 2009, no. 4, 43–49 | MR

[12] Glukhov M. M., “Svobodnye razlozheniya i algoritmicheskie problemy v $R$-mnogoobraziyakh universalnykh algebr”, Matem. sb., 85:3 (1971), 308–338