• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.283-294
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• 2007

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.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.483-494
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• 2012

In this paper we study properties of commutative BE-algebras and we give the construction of quotient (X/I; *, I) of a commutative BE-algebra X via an obstinate ideal I of X. We construct upper semilattice and prove that is a nearlattice. Finally we define and study commutative ideals in BE-algebras.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.541-544
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• 1995

In [1], Ahmad has given a characterization of prime dual ideals in bounded commutative BCK-algebras. The aime of this paper is to show that Theorem of [1] holds without the commutativity.