Iwahori-Hecke algebra of symmetric group:S3

The Iwahori-Hecke algebra of symmetric group:S3 over a commutative unital ring $$R$$ is defined as the $$R[q]$$-algebra:

$$R[q] = \langle T_1,T_2 \rangle/ \langle (T_1 - q)(T_1 + 1), (T_2 - q)(T_2 + 1), T_1T_2T_1 - T_2T_1T_2 \rangle$$

Specializing to $$q = 1$$ gives the group algebra over $$R$$ of symmetric group:S3:

$$R[S_3] = R\langle T_1,T_2,T_3 \rangle/\langle T_1^2 - 1, T_2^2 - 1, T_1T_2T_1 - T_2T_1T_2 \rangle$$

The thing below needs to be fixed