نتایج جستجو برای: free rank
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In this paper we study vector spaces of matrices, all of whose elements have rank at most a given number. The problem of classifying such spaces is roughly equivalent to the problem of classifying certain torsion-free sheaves on projective spaces. We solve this problem in case the sheaf in question has first Chern class equal to 1; the characterization of the vector spaces of matrices of rank d...
In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that dlog2(l)e is a lower bound on the split rank of the int...
BACKGROUND Receptor activator of NFkB (RANK), its ligand (RANKL) and the decoy receptor of RANKL (osteoprotegerin, OPG) play a pivotal role in bone remodeling by regulating osteoclasts formation and activity. RANKL stimulates migration of RANK-expressing tumor cells in vitro, conversely inhibited by OPG. MATERIALS AND METHODS We examined mRNA expression levels of RANKL/RANK/OPG in a publicly ...
We prove that for the free group of rank two F cokernel homomorphism to its Baumslag rationalization ? Bau(F) is not abelian. Moreover, this contains a subgroup countable rank. This answers question Emmanuel Farjoun.
We answer a question due to A. Myasnikov by proving that all expected ranks occur as the ranks of intersections of finitely generated subgroups of free groups. Mathematics Subject Classification (2000): 20E05 Let F be a free group. Let H and K be nontrivial finitely generated subgroups of F . It is a theorem of Howson [1] that H ∩K has finite rank. H. Neumann proved in [2] that rank(H ∩K)− 1 ≤ ...
If A is a stable basis algebra of rank n, then the set Sn−1 of endomorphisms of rank at most n−1 is a subsemigroup of the endomorphism monoid of A. This paper gives a number of necessary and sufficient conditions for Sn−1 to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left T -sets of finite rank where T is can...
In the discussion of A-solvable groups, the question arises if a torsion-free abelian group A of finite rank is flat as a module over its endomorphism ring if every A-generated subgroup of a torsion-free A-solvable group is A-solvable. This paper gives a negative answer by constructing a torsion-free group of rank 3 for which all A-generated torsion-free groups are A-solvable, although A is not...
In this article we formalize a free Z-module and its rank. We formally prove that for a free finite rank Z-module V , the number of elements in its basis, that is a rank of the Z-module, is constant regardless of the selection of its basis. Z-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [15]. Some theo...
In 1937, Baer solved the classification problem for the torsion-free abelian groups of rank 1. Since then, despite the efforts of many mathematicians, no satisfactory solution has been found of the classification problem for the torsion-free abelian groups of rank n ≥ 2. So it is natural to ask whether the classification problem for the higher rank groups is genuinely difficult. In this article...
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