2023/01/27 by Gusev, S. V.
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2301.11863
We show that the following semirings satisfy the same identities: the semiring Rn of all reflexive binary relations on a set with n elements, the semiring Un of all n× n upper triangular matrices over the boolean semiring, the semiring Cn of all order preserving and extensive transformations of a chain with n elements. In view of the result of Klíma and Polák, which states that Cn has a finite basis of identities for all n, this implies that the identities of Rn and Un admit a finite basis as well.