We study small quasi-projective modules and closely related classes of modules. The concept of a small quasi-projective module is dual to the concept of an essentially quasi-injective module, which has recently been studied in several works. It is shown that over right perfect rings, the class of small quasi-projective right modules coincides with a number of classes of right modules close to projective modules, which are studied in the article. As a consequence of the obtained results, the well-known A.A. Tuganbaev’s theorem on the coincidence of the classes of quasi-projective right modules and endomorphism-lifting right modules over right perfect rings is presented. Also, characterizations are obtained for modules M , for which in the category σ[M ] every (finitely generated, cyclic, semisimple, simple) module is small projective in σ[M ].
The article deals with semigroup C∗-algebras generated by regular representations of free products of abelian semigroups. A criterion of the simplicity of this algebras is obtained, characters, grading and a number of other properties are described.
A series of results is presented on the problem of the existence and the uniqueness of extensions of continuous mappings on topological spaces.
We prove that the quasivariety of (0, 1)-lattices generated by the diamant M3 is a variety and find an equational basis of this variety.
Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects in the category of hypergraphic automata are called universal hypergraphic automata. The semigroups of input symbols of such automata are derivative algebras of mappings for such automata. So their properties are interconnected with properties of the algebraic structures of the automata. This paper describes the structure of monomorphisms of such automata and their semigroups of input signals.
In 1993, R. Downey and M. Stob showed that the downwards density of computably enumerable (c.e.) Turing degrees in the partial 2-c.e. Turing degrees cannot be obtained from a uniform construction. We generalize this result for any n > 2 and show that there is no a uniform construction for the downwards density of (n − 1)-c.e. degrees in the structure of n-c.e. degrees. Moreover, we show that there is no a uniform construction for the downwards density in the n-c.e. degrees.
