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Feb 5, 2013 at 18:51 comment added Boris Novikov Babak, in your semigroups all idempotents are central. There are some articles on semigrous with commuting idempotents, e.g. C.Ash, Finite semigroups with commuting idempotents, J. of the Australian Math. Society (1987). Maybe they will be useful for you.
Feb 5, 2013 at 18:20 comment added Mikasa Thanks Boris for the time. I think, I should focus to Clifford's paper again, however it is very old one.
Feb 5, 2013 at 18:18 vote accept Mikasa
Feb 5, 2013 at 15:37 history answered Boris Novikov CC BY-SA 3.0