Geodesic
Lattices of topologies of unary algebras of the variety~$\mathcal A_{1,1}$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 25-32.

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

We consider the variety of unary algebras $\langle A,f,g\rangle$ defined by the identities $f(g(x))=g(f(x))=x$. We describe algebras of this variety, whose lattices of topologies are modular, distributive, linearly ordered, complemented, or pseudocomplemented.
Keywords: unary algebra, lattice of topologies, variety. 
@article{IVM_2009_4_a2,
     author = {A. V. Kartashova},
     title = {Lattices of topologies of unary algebras of the variety~$\mathcal A_{1,1}$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--32},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_4_a2/}
}
TY  - JOUR
AU  - A. V. Kartashova
TI  - Lattices of topologies of unary algebras of the variety~$\mathcal A_{1,1}$
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 25
EP  - 32
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_4_a2/
LA  - ru
ID  - IVM_2009_4_a2
ER  - 
%0 Journal Article
%A A. V. Kartashova
%T Lattices of topologies of unary algebras of the variety~$\mathcal A_{1,1}$
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 25-32
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_4_a2/
%G ru
%F IVM_2009_4_a2
A. V. Kartashova. Lattices of topologies of unary algebras of the variety~$\mathcal A_{1,1}$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 25-32. http://geodesic.mathdoc.fr/item/IVM_2009_4_a2/

[1] Kartashova A. V., “Reshetki topologii unarnykh algebr”, UMN, 55:6 (2000), 141–142 | MR | Zbl

[2] Kartashova A. V., “On lattices of topologies of unary algebras”, J. Math. Sci., 114:2 (2003), 1086–1118 | DOI | MR | Zbl

[3] Kartashova A. V., “Psevdodopolneniya v reshetkakh topologii unarov”, Chebyshevskii sb., 4:1(5) (2003), 85–93 | MR | Zbl

[4] Kartashova A. V., “Analog teoremy Makkenzi dlya reshetok topologii konechnykh algebr”, Fundament. i prikl. matem., 11:3 (2005), 109–117 | MR | Zbl

[5] Akataev A. A., Smirnov D. M., “Reshetki podmnogoobrazii mnogoobrazii algebr”, Algebra i logika, 7:1 (1968), 5–25 | MR | Zbl

[6] Gorbunov V. A., “Pokrytiya v reshetkakh kvazimnogoobrazii i nezavisimaya aksiomatiziruemost”, Algebra i logika, 16:5 (1977), 507–548 | MR | Zbl

[7] Boschenko A. P., Reshetki kongruentsii unarnykh algebr s dvumya operatsiyami $f$ i $g$, udovletvoryayuschimi tozhdestvam $f(g(x))=g(f(x))=x$ ili $g(f(x))= x$, Dep. v VINITI 20.04.98, No 1220-B98, Volgogr. gos. ped. un-t, Volgograd, 1998, 32 pp.

[8] Kartashov V. K., “O reshetkakh kvazimnogoobrazii unarov”, Sib. matem. zhurn., 26:3 (1985), 49–62 | MR | Zbl

[9] Gorbunov V. A., “O reshetke kvazimnogoobrazii”, Algebra i logika, 15:4 (1976), 436–457 | MR | Zbl