It is well known that if a ring has an identity then its prime spectrum is compact and if it does not, the spectrum could be non-compact. There are two standard methods to adjoin an identity to a commutative ring of non-zero characteristic n. Through these methods we obtain two unitary rings: one of characteristic n and the other of characteristic zero. If the spectrum of the original ring is non-compact, then the two spectra of the new rings contain a compactification by finite points of the original spectrum. Although the spectra are different, the two compactifications are homeomorphic.