• Kyungpook Mathematical Journal
• /
• v.47 no.2
• /
• pp.227-237
• /
• 2007

We define weak distributive $n$-semilattices and $n$-lattices, using variants of the absorption law and those of the distributive law. From a weak distributive $n$-semilattice, we construct direct system of subalgebras which are weak distributive $n$-lattices and show that its direct limit is a reflection of the category $wDn$-SLatt of the weak distributive $n$-semilattices.

• Theoretical Mathematics and Pedagogical Mathematics
• /
• v.4 no.2
• /
• pp.131-135
• /
• 1997

We give the relation between the semilattice congruence N and the set of prime ideals of the ordered $\Gamma$-semigroup M.