User talk:Remag121

There are several reasons that mathematical rings should not be defined with a requirement for an identity element. First rings with an identity element have maximal ideals ( maximal right and left ideals). The definitions for right(left) quasiregularity differ. Ring modules need not be unital. Some theorems differ in each case. Remag121 (talk) 18:47, 2 July 2011 (UTC) Note my change to the examples under reduced ring due to an error in the quotient ring example Z[x,y]/(xy) regarding zero divisors using my former email address remag12@yahoo.com.