On 2-von Neumann Regular Rings # |
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| Authors: | Najib Mahdou |
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| Institution: | 1. Département de Mathématiques et Informatique, Faculté des Sciences et Techniques Fès-Sa?ss , Université S.M. Ben Abdellah , Fès, Morocco mahdou@hotmail.com |
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| Abstract: | In this article, we consider 2-von Neumann regular rings, that is, rings R with the property that, if F 2 → F 1 → F 0 → E → 0 is an exact sequence of R-modules with F 0, F 1, and F 2 finitely generated free modules, then the module E is projective. For each positive integer m, as well as for m = ∞, we exhibit a class of 2-von Neumann regular rings with Krull dimension m. For this purpose, we study trivial extensions of local rings by infinite-dimensional vector spaces over their residue fields. The article includes a brief discussion of the scope and precision of our results. |
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