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《Journal of Pure and Applied Algebra》2022,226(4):106862
We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated. 相似文献
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We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the assumption that the abelian surface does not contain low genus curves. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization. 相似文献
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Dikran Dikranjan 《代数通讯》2015,43(1):212-224
Using the nice properties of the w-divisible weight and the w-divisible groups, we prove a factorization theorem for compact abelian groups K; namely, K = K tor × K d , where K tor is a bounded torsion compact abelian group and K d is a w-divisible compact abelian group. By Pontryagin duality this result is equivalent to the same factorization for discrete abelian groups proved in [9]. 相似文献
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Julian Brough 《代数通讯》2013,41(12):5347-5361
Let p be a prime. We prove that if a finite group G has non-abelian Sylow p-subgroups, and the class size of every p-element in G is coprime to p, then G contains a simple group as a subquotient which exhibits the same property. In addition, we provide a list of all the simple groups and primes such that the Sylow p-subgroups are non-abelian and all p-elements have class size coprime to p. 相似文献
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M. Chacron 《代数通讯》2013,41(7):2956-2968
We are given a division ring D with involution (*) and with a *-valuation V such that V(sx ? xs) > V(sx), for all nonzero elements x, s of D with s = s*. Let χ denote the characteristic of the residue class division ring associated with V. We reported in Theorem 3.2.5 Part 4 in [3] that, in the case χ = 0, either D is a standard quaternion division algebra or else D contains no algebraic elements other than the scalars. In this article, we carry out a generalization of the preceding theorem to the case χ ≠ 2. Our results are fairly complete in the finite dimensional case, and generalize theorems of, notably, J. Graeter and A. I. Lichtman, in the infinite dimensional case. 相似文献
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Tararin has shown that a non-Abelian group G admits a nonzero finite number of distinct right-orders if and only if G is equipped with a Tararin-type series of some length n. Further, a group which has a Tararin-type series of length n admits 2 n right-orders. It is known that a group has two right-orders if and only if it is torsionfree Abelian of rank 1. Here we completely classify the groups which admit either four or eight right-orders. 相似文献