Varieties and Nilpotent Extensions of Permutative Periodic Semigroups |
| |
Authors: | Email author" target="_blank">Samuel JL?KopamuEmail author |
| |
Institution: | (1) Department of Mathematics and Computer Science, PNG University of Technology, Private Mail Bag, Lae, Papua New Guinea |
| |
Abstract: | We investigate certain semigroup varieties formed by nilpotent extensions of
orthodox normal bands of commutative periodic groups. Such semigroups are shown
to be both structurally periodic and structurally commutative, and are therefore
structurally inverse semigroups. Such semigroups are also shown to be dense
semilattices of structurally group semigroups. Making use of these structure
decompositions, we prove that the subvariety lattice of any variety comprised of
such semigroups is isomorphic to the direct product of the following three
sublattices: its sublattice of all structurally trivial semigroup varieties, its
sublattice of all semilattice varieties, and its sublattice of all group
varieties. We conclude, therefore, that to completely describe this lattice, we
must first describe completely the lattice of all structurally trivial semigroup
varieties, since the other two are well known lattices. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|