International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 655-660
-systems in local Noether lattices
1Department of Mathematics, University of Iowa, Iowa City 52242, Iowa, USA
2Department of Mathematics, University of Houston, Houston 77204, Texas, USA
3Department of Mathematics and Computer Science, University of Texas-Pan American, Edinburg 78539, Texas, USA
Received 26 April 1993; Revised 7 September 1993
Copyright © 1994 E. W. Johnson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we introduce the concept of a -system in a local Noether lattice and obtain several characterizations of these elements. We first obtain a topological characterization and then a characterization in terms of the existence of a certain type of decreasing sequence of elements. In addition, -systems are characterized in quotient lattices and completions.