A NEW METHOD IN THE FINITE BASIS PROBLEM WITH APPLICATIONS TO RANK 2 TRANSFORMATION SEMIGROUPS
2007 ◽
Vol 17
(07)
◽
pp. 1431-1463
◽
Keyword(s):
Rank 2
◽
We prove that the semigroup of all transformations of a 3-element set with rank at most 2 does not have a finite basis of identities. This gives a negative answer to a question of Shevrin and Volkov. It is worthwhile to notice that the semigroup of transformations with rank at most 2 of an n-element set, where n > 4, has a finite basis of identities. A new method of constructing finite non-finitely based semigroups is developed.
2012 ◽
Vol 49
(3)
◽
pp. 366-389
◽
2015 ◽
Vol 18
(1)
◽
pp. 1-129
◽
Keyword(s):
2008 ◽
Vol 18
(07)
◽
pp. 1193-1201
◽
Keyword(s):
2001 ◽
Vol 44
(1)
◽
pp. 27-47
◽
Keyword(s):
2000 ◽
Vol 10
(04)
◽
pp. 457-480
◽
Keyword(s):
2012 ◽
Vol 29
(3)
◽
pp. 571-590
◽
2008 ◽
Vol 01
(02)
◽
pp. 189-202
◽
1970 ◽
Vol 4
(2)
◽
pp. 381-389
◽