# Talk:Quotient Ring of Ring with Unity is Ring with Unity

There's a rename comment: "Misleading as quotient ring may have unity while the original ring has none." Can there be such an object? --prime mover (talk) 10:24, 28 December 2012 (UTC)

Take e.g. $\Z \times 2 \Z$ with ideal $\{0\} \times 2 \Z$. The ring has no unity, but the quotient ring is iso to $\Z$. --Lord_Farin (talk) 10:40, 28 December 2012 (UTC)
Good call. The above could serve as an proof by example of a page tentatively entitled "Ring Without Unity may have Quotient Ring with Unity" or something so as to clarify. --prime mover (talk) 10:45, 28 December 2012 (UTC)
Ring Without Unity may have Quotient Ring with Unity. --Lord_Farin (talk) 11:30, 31 December 2012 (UTC)