Abstract:
A complete description of the lattice of all antivarieties of unars is given. It is stated that there exist continuum many antivarieties of unars not having an independent basis of identities and a necessary and sufficient condition is specified under which a finite unar has an independent or finite basis of antiidentities. In addition, it is proved that the lattice of all antivarieties of unars is isomorphic to a lattice of A1,1-antivarieties, where A1,1 is a variety of unary algebras of a signature ⟨f,g⟩ defined by identities f(g(x))=g(f(x))=x.
Keywords:
antivariety of unars, lattice, identity.
This publication is cited in the following 6 articles:
A. I. Budkin, “Ob $\omega $-nezavisimosti kvazimnogoobrazii nilpotentnykh grupp”, Sib. elektron. matem. izv., 16 (2019), 516–522
A. I. Budkin, “$\omega$-Independent bases for quasivarieites
of torsion-free groups”, Algebra and Logic, 58:3 (2019), 214–223
A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, “Lattices of subclasses. III”, Sib. elektron. matem. izv., 14 (2017), 252–263
A. O. Basheeva, A. V. Yakovlev, “Ob $\omega$-nezavisimykh bazisakh kvazitozhdestv”, Sib. elektron. matem. izv., 14 (2017), 838–847
A. V. Kravchenko, A. V. Yakovlev, “Quasivarieties of graphs and independent axiomatizability”, Siberian Adv. Math., 28:1 (2018), 53–59
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “On quasi-equational bases for differential groupoids and unary algebras”, Sib. elektron. matem. izv., 14 (2017), 1330–1337