Shades of orthodoxy in Rees-Sushkevich varieties |
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Authors: | Norman R Reilly |
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Institution: | (1) Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada |
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Abstract: | It is shown that, within the class of Rees-Sushkevich varieties that are generated by completely (0-) simple semigroups over
groups of exponent dividing n, there is a hierarchy of varieties determined by the lengths of the products of idempotents that will, if they fall into
a group ℋ-class, be idempotent. Moreover, the lattice of varieties generated by completely (0-) simple semigroups over groups
of exponent dividing n, with the property that all products of idempotents that fall into group ℋ-classes are idempotent, is shown to be isomorphic
to the direct product of the lattice of varieties of groups with exponent dividing n and the lattice of exact subvarieties of a variety generated by a certain five element completely 0-simple semigroup. |
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Keywords: | Semigroup Orthodox Rees-Sushkevich varieties |
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