Short reports
ScienceAsia 36 (2010): 85-88 |doi:
10.2306/scienceasia1513-1874.2010.36.085
Some results on semigroups admitting ring structure
Yupaporn Kemprasita,*, Ngarmcherd Danpattanamongkona, Knograt Savettaseraneeb
ABSTRACT: Lawson has given a sufficient condition for a semigroup S which guarantees that S does not admit a ring structure. From Lawson's theorem, we have that the multiplicative interval semigroup [0,1] does not admit a ring structure. In this paper we give an elementary proof of this fact. We then show that the multiplicative interval semigroup [a,1] with −1≤a<0<a2≤1 does not admit the structure of a ring, a fact which cannot be derived from Lawson's theorem. These facts are then applied to show that every nontrivial multiplicative bounded interval semigroup on ℝ does not admit a ring structure.
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Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand |
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Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand |
* Corresponding author, E-mail: yupaporn.k@chula.ac.th
Received 14 Jul 2009, Accepted 17 Dec 2009
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