Abstract
AbstractIf 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 CSand 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.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
Reference22 articles.
1. [21] Wismath S. , ‘The lattice of varieties and pseudovarieties of band monoids’, Thesis, Simon Fraser University, 1983.
2. On the lattice of varieties of completely simple semigroups
3. [18] Petrich M. and Reilly N. R. , ‘Certain homomorphism of the lattice of varieties of completely simple semigroups’, J. Austral. Math. Soc. (to appear).
4. All varieties of central completely simple semigroups
5. Bands of groups with universal properties
Cited by
33 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献