Iterative Algebras without Projections

We deal with iterative algebras of functions of -valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of -valued logic, for , without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of -valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is.