Characterizing the minimality and maximality of ordered lateral ideals in ordered ternary semigroups
1
조회
0
다운로드
3
인용
0
참고문헌
키워드
초록
In 1932, Lehmer [4] gave the definition of a ternary semigroup. We can see that any semigroup can be reduced to a ternary semigroup. In this paper, we give some auxiliary results which are also necessary for our considerations and characterize the relationship between the (0-)minimal and maximal ordered lateral ideals and the lateral simple and lateral 0-simple ordered ternary semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu [2].
Abstract
In 1932, Lehmer [4] gave the definition of a ternary semigroup. We can see that any semigroup can be reduced to a ternary semigroup. In this paper, we give some auxiliary results which are also necessary for our considerations and characterize the relationship between the (0-)minimal and maximal ordered lateral ideals and the lateral simple and lateral 0-simple ordered ternary semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu [2].
참고문헌 (5)
- M. Arslanov, "A note on minimal and maximal ideals of ordered semigroups", Lobachevskii J. Math., 11, pp.3~6 (2002)
- Y. Cao, "On minimal and maximal left ideals in ordered semigroups", Semigroup Forum, 60(2), pp.202~207 (2000)
- V. N. Dixit, "A note on quasi and bi-ideals in ternary semigroups", Internat. J. Math. Math. Sci., 18(3), pp.501~508 (1995)
- D. H. Lehmer, "A ternary analogue of abelian groups", Amer. J. Math., 54(2), pp.329~338 (1932)
- F. M. Sioson, "Ideal theory in ternary semigroups", Math. Japon., 10, pp.63~84 (1965)