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LEFT MAXIMAL AND STRONGLY RIGHT MAXIMAL IDEMPOTENTS IN G*

  • YEVHEN ZELENYUK (a1)

Abstract

Let G be a countably infinite discrete group, let βG be the Stone–Čech compactification of G, and let ${G^{\rm{*}}} = \beta G \setminus G$ . An idempotent $p \in {G^{\rm{*}}}$ is left (right) maximal if for every idempotent $q \in {G^{\rm{*}}}$ , pq = p (qp = P) implies qp = q (qp = q). An idempotent $p \in {G^{\rm{*}}}$ is strongly right maximal if the equation xp = p has the unique solution x = p in G*. We show that there is an idempotent $p \in {G^{\rm{*}}}$ which is both left maximal and strongly right maximal.

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[1] Ellis, R., Lectures on Topological Dynamics, Benjamin, New York, 1969.
[2] Hindman, N. and Strauss, D., Nearly prime subsemigroups of β. Semigroup Forum, vol. 51 (1995), pp. 299318.
[3] Hindman, N. and Strauss, D., Algebra in the Stone-Čech Compactification, De Gruyter, Berlin, 1998.
[4] Protasov, I., Maximal topologies on groups . Siberian Mathematical Journal, vol. 39 (1998), pp. 11841194.
[5] Ruppert, W., Compact Semitopological Semigroups: An Intrinsic Theory, Lecture Notes in Mathematics 1079, Springer-Verlag, Berlin, 1984.
[6] Zelenyuk, Y., Ultrafilters and Topologies on Groups, De Gruyter, Berlin, 2011.
[7] Zelenyuk, Y., Principal left ideals of βG may be both minimal and maximal . Bulletin of the London Mathematical Society, vol. 45 (2013), pp. 613617.
[8] Zelenyuk, Y., Left maximal idempotents in G * . Advances in Mathematics, vol. 262 (2014), pp. 593603.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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