The Hopkins-Levitzky theorem states that Artinian rings are necessarily Noetherian. Under certain conditions results about the opposite implication, namely which Noetherian rings are necessarily Artinian, can be derived. This paper is devoted to a reflection of these problems within the synthetic framework of projective lattice geometry as it has first been established in.
|Title of host publication||Algebra and its applications|
|Editors||D. V. Huynh, S. K. Jain , S. R. López-Permouth|
|Number of pages||6|
|Publication status||Published - 2000|
|Publisher||Amer. Math. Soc., Providence, RI|