In this paper, we obtain a Gröbner-Shirshov (noncommutative Gröbner) basis for the singular part of the Brauer semigroup. It gives an algorithm for getting normal forms and hence an algorithm for solving the word problem in these semigroups.
ATEŞ, FIRAT; ÇEVİK, AHMET SİNAN; and KARPUZ, EYLEM GÜZEL
"Gröbner-Shirshov basis for the singular part of the Brauer semigroup,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 47.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/47