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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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a Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
b 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