On semigroups admitting ring structure
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- 作者：Ryszard Mazurek (1) r.mazurek@pb.edu.pl
- 关键词：Semigroup admitting a ring structure – ; Right ; chain semigroup – ; Multiplicative interval semigroup
- 刊名：Semigroup Forum
- 出版时间：October 2011
- 出版年：2011
- 期刊代码：134_0037-1912
- 类别：mat
- 卷：83
- 期：2
- 页码：335-342
- 数据来源：sp
摘要
A right-chain semigroup is a semigroup whose right ideals are totally ordered by set inclusion. The main result of this paper says that if S is a right-chain semigroup admitting a ring structure, then either S is a null semigroup with two elements or sS=S for some s∈S. Using this we give an elementary proof of Oman’s characterization of semigroups admitting a ring structure whose subsemigroups (containing zero) form a chain. We also apply this result, along with two other results proved in this paper, to show that no nontrivial multiplicative bounded interval semigroup on the real line ℝ admits a ring structure, obtaining the main results of Kemprasit et al. (ScienceAsia 36: 85–88, 2010).