50 research outputs found

    An algorithmic approach to the existence of ideal objects in commutative algebra

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    The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn's lemma, and thus pose a challenge from a computational point of view. Giving a constructive meaning to ideal objects is a problem which dates back to Hilbert's program, and today is still a central theme in the area of dynamical algebra, which focuses on the elimination of ideal objects via syntactic methods. In this paper, we take an alternative approach based on Kreisel's no counterexample interpretation and sequential algorithms. We first give a computational interpretation to an abstract maximality principle in the countable setting via an intuitive, state based algorithm. We then carry out a concrete case study, in which we give an algorithmic account of the result that in any commutative ring, the intersection of all prime ideals is contained in its nilradical

    A possible role for miRNA silencing in disease phenotype variation in Swedish transthyretin V30M carriers

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    Our results are the first to show the presence of a 3'UTR polymorphism on the V30M haplotype in Swedish carriers, which can serve as a miRNA binding site potentially leading to down-regulated expression from the mutated TTR allele. This finding may be related to the low penetrance and high age at onset of the disease observed in the Swedish patient population
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