MONOTONE FAMILIES ON CYCLIC SEMIGROUPS
Keywords:
cyclic semigroup, monotone family, Stone- C ech extension.Abstract
Given a cyclic semigroup S we study right and left zeros, singleton left ideals, the minimal ideal, central elements, left cancelable and right cancelable elements of extensions υ (S ) and characterize cyclic semigroups whose superextensions are commutative.
References
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2. Banakh T. Algebra in superextension of groups, II: cancelativity and centers / T.Banakh, V.Gavrylkiv // Algebra Discrete Math. – 2008. – No.4. – Р. 1-14.
3. Banakh T. Algebra in superextension of groups: minimal left ideals / T.Banakh, V.Gavrylkiv // Mat. Stud. – 31 (2009). – Р. 142-148.
4. Banakh T. Algebra in the superextensions of twinic groups / T.Banakh, V.Gavrylkiv // Dissert. Math. – 473 (2010). – 74 pp.
5. Banakh T. Algebra in superextensions of semilattices / T.Banakh, V.Gavrylkiv // Algebra Discrete Math. – 13:1 (2012). – Р. 26-42.
6. Banakh T. Algebra in superextensions of inverse semigroups, / T.Banakh, V.Gavrylkiv // Algebra Discrete Math. – 13:2 (2012). – Р. 147-168.
7. Clifford A.H. The algebraic theory of semigroups. Vol. I. / A.H.Clifford, G.B.Preston / Mathematical Surveys. – 7. AMS, Providence, RI, 1961.
8. Gavrylkiv V. The spaces of inclusion hyperspaces over noncompact spaces / V.Gavrylkiv // Mat. Stud. – 28:1 (2007). – Р. 92-110.
9. Gavrylkiv V. Right-topological semigroup operations on inclusion hyperspaces / V.Gavrylkiv // Mat. Stud. – 29:1 (2008). – Р. 18-34.
10. Gavrylkiv V. On representation of semigroups of inclusion hyperspaces / V.Gavrylkiv // Carpathian Mathematical Publication. – 2:1 (2010). – Р. 24-34.
11. Hindman N. Algebra in the Stone- C ech compactification, de Gruyter / N.Hindman, D.Strauss. – Berlin, New York, 1998.
12. Teleiko A. Categorical Topology of Compact Hausdorff Spaces A.Teleiko, M.Zarichnyi. – VNTL, Lviv, 1999.
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Published
2019-03-07
How to Cite
Гаврилків, В. М. (2019). MONOTONE FAMILIES ON CYCLIC SEMIGROUPS. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (1(17), 102–112. Retrieved from https://pvntsh.nung.edu.ua/index.php/number/article/view/236
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Section
Mathematics and Mechanics
