Automorphisms of the endomorphism semigroup of a free commutative g-dimonoid

Fri, 01 Jan 2016 00:00:00 GMT

Automorphisms of the endomorphism semigroup of a free commutative g-dimonoid Zhuchok, Y.V. We determine all isomorphisms between the endomorphism semigroups of free commutative g-dimonoids and prove that all automorphisms of the endomorphism semigroup of a free commutative g-dimonoid are quasi-inner.

The comb-like representations of cellular ordinal balleans

Fri, 01 Jan 2016 00:00:00 GMT

The comb-like representations of cellular ordinal balleans Protasov, I.; Protasova, K. Given two ordinal λ and γ, let f:[0,λ)→[0,γ) be a function such that, for each α<γ, sup{f(t):t∈[0,α]}<γ. We define a mapping df:[0,λ)×[0,λ)⟶[0,γ) by the rule: if x

On a semitopological polycyclic monoid

Fri, 01 Jan 2016 00:00:00 GMT

On a semitopological polycyclic monoid Bardyla, S.; Gutik, O. We study algebraic structure of the λ-polycyclic monoid Pλ and its topologizations. We show that the λ-polycyclic monoid for an infinite cardinal λ≥2 has similar algebraic properties so has the polycyclic monoid Pn with finitely many n≥2 generators. In particular we prove that for every infinite cardinal λ the polycyclic monoid Pλ is a congruence-free combinatorial 0-bisimple 0-E-unitary inverse semigroup. Also we show that every non-zero element x is an isolated point in (Pλ,τ) for every Hausdorff topology τ on Pλ, such that (Pλ,τ) is a semitopological semigroup, and every locally compact Hausdorff semigroup topology on Pλ is discrete. The last statement extends results of the paper [33] obtaining for topological inverse graph semigroups. We describe all feebly compact topologies τ on Pλ such that (Pλ,τ) is a semitopological semigroup and its Bohr compactification as a topological semigroup. We prove that for every cardinal λ≥2 any continuous homomorphism from a topological semigroup Pλ into an arbitrary countably compact topological semigroup is annihilating and there exists no a Hausdorff feebly compact topological semigroup which contains Pλ as a dense subsemigroup.

Mykola Komarnytskyi (25.05.1948 — 21.04.2016)

Fri, 01 Jan 2016 00:00:00 GMT

Mykola Komarnytskyi (25.05.1948 — 21.04.2016) Distinguished Professor of Ivan Franko L'viv National University, Doctor of Sciences Mykola Komarnytskyi passed away on April 21, 2016. His sudden death is a great loss for L'viv mathematicians and for the entire Ukrainian mathematics community.

Algebra and Discrete Mathematics, 2016, Vol. 21, № 2

Automorphisms of the endomorphism semigroup of a free commutative g-dimonoid

The comb-like representations of cellular ordinal balleans

On a semitopological polycyclic monoid

Mykola Komarnytskyi (25.05.1948 — 21.04.2016)