39 research outputs found
Presentation of the singular part of the Brauer monoid
We obtain a presentation for the singular part of the Brauer monoid with
respect to an irreducible system of generators, consisting of idempotents. As
an application of this result we get a new construction of the symmetric group
via connected sequences of subsets. Another application describes the lengths
of elements in the singular part of the Brauer monoid with respect to the
system of generators, mentioned above.Comment: 22 page
Monoids admit finite complete rewriting systems
The aim of this note is to prove that monoids , with of relative length 6, admit finite complete
rewriting systems. This is some advance in the understanding the long-standing
open problem whether the word problem for one-relator monoids is soluble