Topic
Null semigroup
About: Null semigroup is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 2 citations. The topic is also known as: zero semigroup.
Papers
TL;DR: The main result of Kemprasit et al. as discussed by the authors is that if a right-chain semigroup admits a ring structure, then either S is a null semigroup with two elements or sS=S for some s∈S.
Abstract: 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).
2 citations
TL;DR: In this paper, the authors characterized the finite nilpotent semigroups by the length of the ideal lattice of ideals of a null semigroup and generalized a theorem of T. Tamura and M. Yamada.
Abstract: In this paper, we establish several properties of the lattice of ideals of a nilpotent semigroup. In particular, we characterize the finite nilpotent semigroups by the length of this lattice, and we generalize a theorem of T. Tamura and M. Yamada [5], concerning the ideal extension of a nilpotent semigroup by a null semigroup.
Performance Metrics
| Year | Papers |
|---|---|
| 2011 | 1 |
| 1972 | 1 |