Monolithic modules over Noetherian Rings
Paula A.A.B. Carvalho, Ian M. Musson
TL;DR
This paper investigates finiteness conditions on essential extensions of simple modules over certain noncommutative algebras, improving previous results for down-up algebras.
Contribution
It provides new insights into the structure of modules over quantum plane, quantized Weyl algebra, and Noetherian down-up algebras, extending earlier work.
Findings
Enhanced finiteness conditions established for modules over these algebras.
Improved results specifically for Noetherian down-up algebras.
Broader understanding of module extensions in noncommutative algebra.
Abstract
We study finiteness conditions on essential extensions of simple modules over the quantum plane, the quantized Weyl algebra and Noetherian down-up algebras. The results achieved improve the ones obtained in [arXiv:0906.2930] for down-up algebras.
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