- Near λ-lattices
- Near λ-lattices
- ㆍ 저자명
- Chajda. Ivan,Kolarik. M.
- ㆍ 간행물명
- Kyungpook mathematical journal
- ㆍ 권/호정보
- 2007년|47권 2호|pp.283-294 (12 pages)
- ㆍ 발행정보
- 경북대학교 자연과학대학 수학과
- ㆍ 파일정보
- 정기간행물|ENG| PDF텍스트
- ㆍ 주제분야
- 기타
By a near ${lambda}$-lattice is meant an upper ${lambda}$-semilattice where is defined a parti binary operation $x{Lambda}y$ with respect to the induced order whenever $x$, $y$ has a common lower bound. Alternatively, a near ${lambda}$-lattice can be described as an algebra with one ternary operation satisfying nine simple conditions. Hence, the class of near ${lambda}$-lattices is a quasivariety. A ${lambda}$-semilattice $mathcal{A}=(A;{vee})$ is said to have sectional (antitone) involutions if for each $a{in}A$ there exists an (antitone) involution on [$a$, 1], where 1 is the greatest element of $mathcal{A}$. If this antitone involution is a complementation, $mathcal{A}$ is called an ortho ${lambda}$-semilattice. We characterize these near ${lambda}$-lattices by certain identities.