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/lp/springer-journals/on-the-boundary-of-algebraic-radicals-in-topological-semigroups-pi40fg5Zyn
- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Mathematics, general
- ISSN
- 0001-5954
- eISSN
- 1588-2632
- DOI
- 10.1007/BF01901741
- Publisher site
- See Article on Publisher Site
Abstract
Acta Mathematica Academiae Scientiarum Hungaricae Tomus 25 (1--2), (1974), pp. 15--19. ON THE BOUNDARY OF ALGEBRAIC RADICALS IN TOPOLOGICAL SEMIGROUPS By K.-P. SHUM (Hong Kong) A topological semigroup is a semigroup with a Hausdorff topology in which multiplication is continuous in both variables. In what follows S will denote a topological semigroup. We let A be any subset of S. The algebraic radical of A is defined to be the set {xCS]xkEA for some integer k_->l} and is denoted by R(A). In [3], K. P. SHUM and C. S. Hoo studied some properties of the algebraic radicals of ideals in compact abelian semigroups. In this paper, we are going to give further investigations on the algebraic radical of an ideal A of S. We find that the boundary of the algebraic radical of an open ideal A of S is closely related with a compact group in S. But in general, the structure of such a compact group is still not known to the author. Here only the existence of a compact group on the boundary of R (A) will be discussed. We list here several definitions which will be frequently used in this paper. Let A be any
Journal
Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals
Published: Jun 18, 2005