On a semitopological polycyclic monoid

• Дата: 2016
• Автори: Bardyla, S., Gutik, O.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут прикладної математики і механіки НАН України 2016
• Назва видання: Algebra and Discrete Mathematics
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/155255
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: On a semitopological polycyclic monoid / S. Bardyla, O. Gutik // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 163-183. — Бібліогр.: 38 назв. — англ.

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.