Hyperidentities for some varieties of semigroups (Q583257)

For a variety V of semigroups, \(\bar V\) denotes the largest variety of semigroups containing V and generating the same hypervariety (in the sense of W. Taylor) as V. If \(V=\bar V\) then V is called closed. The closure \(\bar V\) is found for any variety V of bands and also for any nilpotent variety \(V=N_ k\) (determined by \(x_ 1...x_ k=y_ 1...y_ k)\). For a nontrivial closed variety V of bands and any k, the join \(V\vee N_ k\) is proved to be also closed.