Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1985 · 38 citations · 16 references
Natural SciencesMathematicsAlgebraRepresentation TheorySet TheoryAbstract AlgebraAlgebraic StructuresCommutative AlgebraGroup TheoryAssociative AlgebrasMonoid TheoryOperatorsSemigroup TheoryVarieties Of Algebras
Abstract If CS (respectively, O ) denotes the class of all completely simple semigroups (respectively, semigroups that are orthodox unions of groups) then CS (respectively, O ) is a variety of algebras with respect to the operations of multiplication and inversion. The main result shows that the lattice of subvarieties of is a precisely determined subdirect product of the lattice of subvarieties of CS and the lattice of subvarieties of O . A basis of identities is obtained for any variety in terms of bases of identities for . Several operators on the lattice of subvarieties of are also introduced and studied.
16
T. E. Hall · Journal of Algebra · 1973 · 220 citations
The lattice of equational classes of idempotent semigroups
J. A. Gerhard · Journal of Algebra · 1970 · 162 citations
Varieties of idempotent semigroups
A. P. Biryukov · Algebra and Logic · 1970 · 103 citations
On the lattice of varieties of bands of groups
T. E. Hall, Peter R. Jones · Pacific Journal of Mathematics · 1980 · 67 citations · Full text
Varieties of orthodox bands of groups
Mario Petrich · Pacific Journal of Mathematics · 1975 · 59 citations · Full text