Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
10.22034/jfmt.2026.604506.1037
Abstract
It is well-known that every Artinian lattice is Loewy but not necessarily Noetherian. For a compactly generated Artinian lattice we determine its deviation from being Noetherian in terms of its Loewy length: we show that a compactly generated Artinian lattice L is λ-Noetherian, where λ is the least regular cardinal greater than the Loewy length of L. Along the way we develop the basic theory of λ-Noetherian lattices (for λ a regular cardinal) in the setting of compactly generated lattices, relate the invariants Gdim, thick and gof a lattice to its Loewy length, and, as an application of these techniques, obtain a lattice-theoretic generalization of a theorem of Armendariz on rings with the descending chain condition on essential (left) ideals.
Motamedi, M., Namdari, M. & Shirali, N. (2027). Ascending chains in Artinian lattices. Journal of Frame and Matrix Theory, 3(1), 121–137. https://doi.org/10.22034/jfmt.2026.604506.1037
MLA
Motamedi, M., Namdari, M., & Shirali, N. "Ascending chains in Artinian lattices", Journal of Frame and Matrix Theory, 3, 1, 2027, 121–137. doi: 10.22034/jfmt.2026.604506.1037
HARVARD
Motamedi, M., Namdari, M., & Shirali, N. (2027). 'Ascending chains in Artinian lattices', Journal of Frame and Matrix Theory, 3(1), pp. 121–137. doi: 10.22034/jfmt.2026.604506.1037
CHICAGO
Motamedi, M., Namdari, M. & Shirali, N., "Ascending chains in Artinian lattices." Journal of Frame and Matrix Theory, 3 1 (2027): 121–137, doi: 10.22034/jfmt.2026.604506.1037
VANCOUVER
Motamedi M., Namdari M., Shirali N. Ascending chains in Artinian lattices. JFMT. 2027;3(1):121–137. doi: 10.22034/jfmt.2026.604506.1037
