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On Monoids of Injective Partial Cofinite Selfmaps

  • Oleg Gutik EMAIL logo and Dušan Repovš
Published/Copyright: December 9, 2015
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 65 Issue 5

Abstract

We study the semigroup Icfλ of injective partial cofinite selfmaps of an infinite cardinal λ. We show that Icfλ is a bisimple inverse semigroup and each chain of idempotents in Icfλ is contained in a bicyclic subsemigroup of Icfλ , we describe the Green relations on Icfλ and we prove that every non-trivial congruence on Icfλ is a group congruence. Also, we describe the structure of the quotient semigroup Icfλ /σ, where σ is the least group congruence on Icfλ.

Keywords: bicyclic semigroup; semigroup of bijective partial transformations; congruence; symmetric group; group congruence; semidirect product

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Received: 2012-10-23
Accepted: 2012-11-22
Published Online: 2015-12-9
Published in Print: 2015-10-1

Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Finite Mixed Sums wih Harmonic Terms
  2. Packing of ℝ2 by Crosses
  3. On the Integrality of the Elementary Symmetric Functions of 1, 1/3, . . . , 1/(2n − 1)
  4. Generalized Derivations as a Generalization of Jordan Homomorphisms Acting on Lie Ideals and Right Ideals
  5. Generalized Derivations on Lie Ideals and Power Values on Prime Rings
  6. On Monoids of Injective Partial Cofinite Selfmaps
  7. Extensions of Dynamic Inequalities of Hardy’s Type on Time Scales
  8. The Controlled Convergence Theorem for the Gap-Integral
  9. The Solvability of a Nonlocal Boundary Value Problem
  10. Oscillation Criteria for Third Order Differential Equations with Functional Arguments
  11. Asymptotic Behavior of Solutions of a Nonlinear Neutral Generalized Pantograph Equation with Impulses
  12. On Null Lagrangians
  13. Principal Eigenvalues for Systems of Schrödinger Equations Defined in the whole Space with Indefinite Weights
  14. Convergence of Series on Large Set of Indices
  15. On Approximation Properties of a New Type of Bernstein-Durrmeyer Operators
  16. Representation of Extendible Bilinear Forms
  17. Spectra and Fine Spectra of Lower Triangular Double-Band Matrices as Operators on Lp (1 ≤ p < ∞)
  18. Topological Fundamental Groups and Small Generated Coverings
  19. A Relation between two Kinds of Norms for Martingales
  20. Linearization Regions in Singular Weakly Nonlinear Regression Models with Constraints
  21. Parametric Equilibrium Problems Governed by Topologically Pseudomonotone Bifunctions
  22. Identification of a Parameter in Fourth-Order Partial Differential Equations by an Equation Error Approach
https://doi.org/10.1515/ms-2015-0067
Keywords for this article
bicyclic semigroup; semigroup of bijective partial transformations; congruence; symmetric group; group congruence; semidirect product

Articles in the same Issue

  1. Finite Mixed Sums wih Harmonic Terms
  2. Packing of ℝ2 by Crosses
  3. On the Integrality of the Elementary Symmetric Functions of 1, 1/3, . . . , 1/(2n − 1)
  4. Generalized Derivations as a Generalization of Jordan Homomorphisms Acting on Lie Ideals and Right Ideals
  5. Generalized Derivations on Lie Ideals and Power Values on Prime Rings
  6. On Monoids of Injective Partial Cofinite Selfmaps
  7. Extensions of Dynamic Inequalities of Hardy’s Type on Time Scales
  8. The Controlled Convergence Theorem for the Gap-Integral
  9. The Solvability of a Nonlocal Boundary Value Problem
  10. Oscillation Criteria for Third Order Differential Equations with Functional Arguments
  11. Asymptotic Behavior of Solutions of a Nonlinear Neutral Generalized Pantograph Equation with Impulses
  12. On Null Lagrangians
  13. Principal Eigenvalues for Systems of Schrödinger Equations Defined in the whole Space with Indefinite Weights
  14. Convergence of Series on Large Set of Indices
  15. On Approximation Properties of a New Type of Bernstein-Durrmeyer Operators
  16. Representation of Extendible Bilinear Forms
  17. Spectra and Fine Spectra of Lower Triangular Double-Band Matrices as Operators on Lp (1 ≤ p < ∞)
  18. Topological Fundamental Groups and Small Generated Coverings
  19. A Relation between two Kinds of Norms for Martingales
  20. Linearization Regions in Singular Weakly Nonlinear Regression Models with Constraints
  21. Parametric Equilibrium Problems Governed by Topologically Pseudomonotone Bifunctions
  22. Identification of a Parameter in Fourth-Order Partial Differential Equations by an Equation Error Approach
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