• On the Warne extension of a monoid
  • In the report the reporter will introduce the Warne extension of a monoid. Also she will discuss the algebraic properties of such semigroup extension.

• Congruense-prime and classical prime acts over a duo-monoid
  • This talk is based on my join work with G. Zelisko and M. Komarnyts'kyy. Some connection between distinct types of prime acts and their properties are established. Notion of a congruence-prime act will be defined. Also I obtains some properties of congruence-prime acts over a duo-monoid with zero and Cohen's type theorems for classical prime acts will be proved.

• On the monoid of co-finite monotone partial bujections of nx_lexZ
  • The structure the monoid of co-finite monotone partial bujections of nx_lexZ is pesented.

• Zharisky-like topology on the classical prime spectrum of a module
  • Classical prime submodules, classical top modules and their properties are studied.

• Pseudocompact topological Brandt λ⁰-extensions of semitopological semigroups
  • We introduce pseudocompact topological Brandt λ⁰-extensions of pseudocompact semitopological semigroups in the class of semitopological semigroups. We establish the structure of pseudocompact topological Brandt λ⁰-extensions of semitopological semigroups, theirs Stone-Čech compactifocations, and categories.

• On H-complete topological semilattices
  • We discussed on H-completenness in General Topolgy and Topological Algebra and give an answer on Question 17 posed in the paper: J. W. Stepp, Algebraic maximal semilattices, Pacific J. Math. 58 (1975), no. 1, 243–248.

• On the semigroup C=< a,b | a² b=a, ab ² =b> as an analoque of the bicyclic semigroup
  • In the report we discuss the property of the semigroup C=< a,b | a² b=a, ab ² =b>, it semigroup topologizations and embeddings into compact-like topological (semitopological) semigroups.

• Models theory of operands: problems and first results in the case of radical and semi-simple classes
  • We give some conditions for the axiomatizability of periodic and torsion free classes in the category of operands over monoids with zero.