In a course in abstract algebra in which the instructor presents a proof that each ideal in a ring with identity is contained in a maximal ideal, it is customary to give an example of a ring without maximal ideals.
© 1975 Mathematical Association of America
Henriksen, Melvin. "A simple characterization of commutative rings without maximal ideals." American Mathematical Monthly 82.5 (1975): 502-505.