Incidence structures of independent sets
Incidence structures of type
Every incidence structure (understood as a triple of sets , ) admits for every positive integer an incidence structure where () consists of all independent -element subsets in () and is determined by some bijections. In the paper such incidence structures are investigated the ’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets and .
Infinite algebras with 3-transitive groups of weak automorphisms
The infinite algebras with 3-transitive groups of weak automorphisms are investigated. Among others it is shown that if an infinite algebra with 3-transitive group of weak automorphisms has a nontrivial idempotent polynomial operation then either it is locally functionally complete or it is polynomially equivalent to a vector space over the two element field or it is a simple algebra that is semi-affine with respect to an elementary 2-group. In the second and third cases the group of weak automorphisms...
Invariants of the rational equivalence.
Large systems of independent objects in concrete categories. II
Large systems of independent objects in concrete categories. I
Lifts for semigroups of endomorphisms of an independence algebra
For a universal algebra , let End() and Aut() denote, respectively, the endomorphism monoid and the automorphism group of . Let S be a semigroup and let T be a characteristic subsemigroup of S. We say that ϕ ∈ Aut(S) is a lift for ψ ∈ Aut(T) if ϕ|T = ψ. For ψ ∈ Aut(T) we denote by L(ψ) the set of lifts of ψ, that is, Let be an independence algebra of infinite rank and...
Lifts for semigroups of monomorphisms of an independence algebra
For a universal algebra 𝓐, let End(𝓐) and Aut(𝓐) denote, respectively, the endomorphism monoid and the automorphism group of 𝓐. Let S be a semigroup and let T be a characteristic subsemigroup of S. We say that ϕ ∈ Aut(S) is a lift for ψ ∈ Aut(T) if ϕ|T = ψ. For ψ ∈ Aut(T) we denote by L(ψ) the set of lifts of ψ, that is, L(ψ) = {ϕ ∈ Aut(S) | ϕ|T = ψ}. Let 𝓐 be an independence algebra of infinite rank and let S be a monoid of monomorphisms such that G = Aut(𝓐) ≤ S ≤ End(𝓐). In [2] it is proved...
Morphisms of a certain class of monounary algebras
On a simple one-element extension of left zero semigroups
On automorphism groups of planar lattices
The structure of automorphisms of planar lattices is analyzed.
On automorphism groups of relational systems and universal algebras
On automorphisms of computability potential scales for -element algebras.
On connected unars with regular endomorphism monoids
On direct limit classes of algebras
On extending endomorphisms to automorphisms.
On functions commuting with semigroups of transformations of algebras.
On independence of the relations of epimorphy and embeddability on the variety of all lattices.
On some constructions of algebraic objects
Mono-unary algebras may be used to construct homomorphisms, subalgebras, and direct products of algebras of an arbitrary type.
On some properties of genomorphisms of -algebras