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    Carvalho, Paula A. A. B. Hatipoğlu, Can and Lomp, Christian 2015. Injective Hulls of Simple Modules over Differential Operator Rings. Communications in Algebra, Vol. 43, Issue. 10, p. 4221.


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    CARVALHO, PAULA A. A. B. and MUSSON, IAN M. 2011. MONOLITHIC MODULES OVER NOETHERIAN RINGS. Glasgow Mathematical Journal, Vol. 53, Issue. 03, p. 683.


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    Lenagan, T. H. 1994. Stability of Gelfand–Kirillov dimension for rings with the strong second layer condition. Proceedings of the Edinburgh Mathematical Society, Vol. 37, Issue. 02, p. 347.


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Some examples of modules over Noetherian rings

  • I. M. Musson (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500004730
  • Published online: 01 May 2009
Abstract

The purpose of this note is to prove the following result.

Theorem 1. Let n be an integer greater than zero. There exists a prime Noetherian ring R of Krull dimension n + 1 and a finitely generated essential extension W of a simple R-module V suchthat

(i) W has Krull dimension n, and

(ii) W/V is n-critical and cannot be embedded in any of its proper submodules.

We refer the reader to [6] for the definition and properties of Krull dimension.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

3.J. Dixmier , Enveloping algebras (North Holland, 1977).

5.K. R. Goodearl , Incompressible critical modules, Comm. Algebra, 8 (1980), 18451852.

7.A. V. Jategaonkar , Jacobson's conjecture and modules over fully bounded Noetherian rings, J. Algebra 30 (1974), 103121.

8.I. M. Musson , Injective modules for group rings of polycyclic groups II, Quart. J. Math. Oxford (2), 31 (1980), 449466.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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