کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4595745 | 1630748 | 2016 | 17 صفحه PDF | دانلود رایگان |
Very flat and contraadjusted modules naturally arise in algebraic geometry in the study of contraherent cosheaves over schemes. Here, we investigate the structure and approximation properties of these modules over commutative noetherian rings. Using an analogy between projective and flat Mittag-Leffler modules on one hand, and very flat and locally very flat modules on the other, we prove that each of the following statements are equivalent to the finiteness of the Zariski spectrum Spec(R)Spec(R) of a noetherian domain R: (i) the class of all very flat modules is covering, (ii) the class of all locally very flat modules is precovering, and (iii) the class of all contraadjusted modules is enveloping. We also prove an analog of Pontryagin's Criterion for locally very flat modules over Dedekind domains.
Journal: Journal of Pure and Applied Algebra - Volume 220, Issue 12, December 2016, Pages 3910–3926