Some examples from infinite matrix rings

Robert W. Miller, Darrel R. Turnidge
1973 Proceedings of the American Mathematical Society  
Examples are given of the following: (1) an injective Noetherian right module which is not Artinian, (2) a linearly compact Noetherian right module over a right perfect ring which is not Artinian, and (3) a (linearly compact) Artinian left module over a right perfect ring which is not Noetherian. These examples answer questions posed by J. W. Fisher and F. L Sandomierski in the Proceedings of the Utah Conference on Ring Theory held in 1971. The purpose of this note is to present two types of
more » ... ent two types of examples. The first is an example of an injective Noetherian right module which is not Artinian. In investigating chain conditions on injective modules [4], the authors were unable to locate an example of such a module in the literature. In the recent Proceedings of the Utah Conference on Ring Theory held in 1971, J. W. Fisher poses as an open question the existence of such a module [3, p. 378].
doi:10.1090/s0002-9939-1973-0310001-3 fatcat:yso3bgdzp5czhdau3o6yv77opy