Global Theory of Lattice-Finite Noetherian Rings |
| |
Authors: | Wolfgang Rump |
| |
Affiliation: | (1) Faculty of Mathematics and Physics, Institute for Algebra and Number Theory, Pfaffenwaldring 57, D-70550 Stuttgart, Germany |
| |
Abstract: | We introduce and study lattice-finite Noetherian rings and show that they form a onedimensional analogue of representation-finite Artinian rings. We prove that every lattice-finite Noetherian ring R has Krull dimension ≼ 1, and that R modulo its Artinian radical is an order in a semi-simple ring. Our main result states that maximal overorders of R exist and have to be Asano orders, while they need not be fully bounded. This will be achieved by means of an idempotent ideal I(R), an invariant or R which is new even for classical orders R. This ideal satisfies I(R) = R whenever R is maximal. Presented by H. Tachikawa |
| |
Keywords: | Primary: 16G30, 16P40, 16N60 Secondary: 16H05 |
本文献已被 SpringerLink 等数据库收录! |
|