sentences:  The ring "A" is a local domain of dimension 2 with maximal ideal "I", so is catenary because all 2-dimensional local domains are catenary.The ring "A" is Noetherian because "B" is Noetherian and is a finite "A"-module.However "A" is not universally catenary, because if it were then the ideal "mB" of "B" would have the same height as "mB"∩"A" by the dimension formula for universally catenary rings, but the latter ideal has height equal to dim("A")=2.