Congruences and on an algebra A are called 2.5-permut-able if the join of and in the lattice of congruences on A coincides with the set-theoretical union of the relations and . A semigroup variety V is called almost fi-permutable [almost weakly fi-permutable, almost fi-2.5-permutable] if any two fully invariant congruences on a V-free object S permute [weakly permute, 2.5-permute] whenever these congruences are contained in the least semilattice congruence on S. We completely determine all almost fi-permutable varieties, all almost fi-2.5-permutable varieties, and almost weakly fi-permutable varieties under the additional assumption that all nilsemigroups in a variety are semigroups with zero multiplication. The first and the third of the corresponding results correct some gaps in two previous papers.
|Translated title of the contribution||Three weaker variants of congruence permutability for semigroup verieties|
|Number of pages||38|
|Journal||Siberian Electronic Mathematical Reports|
|Publication status||Published - 2014|
Level of Research Output
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