U = self._free_module.submodule(ppts) d2 = U.rank()ifd2 != d:# not full dim# we compute two matrices# M1: small space -> big space (makes decomposition)# M2: big space -> small space (i.e. basis of the module)# warning: matrices act on row vectors, i.e. left actionfrom...
(1990): Stably free modules of “big rank” over polynomial rings are free. J. Pure Appl. Algebra 66 (1990), 311–314. MR 91h:13007 (Reviewer: K. Koh) MATH MathSciNetNaude C G, Naude G. Stably free modules of big rank over polynomial rings are free. J Pure Appl Algebra, 66:...
Projective modules over free groups are free In this paper we show that if A is an affine algebra of dimension n over an algebraically closed field, then each stably free module whose rank is greater than or equal to n is free. We also obtain some results on orbits of unimodular ro......
We prove that all pure submodules of a finite rank torsion-free module $A$\nover a Dedekind domain are $A$-generated if and only if $A$ has a rank $1$\ndirect summand $B$ such that $\\mathbf{type}(B)$ is the inner type of $A$. S Breaz 被引量: 0发表: 2018年 The torsio...
The effect of free boundary conditions on the Ising model in high dimensions (1) 57:01 The Effect of Free Boundary Conditions on the Ising Model in High Dimensions 31:49 How round is a Jordan curve_ 54:24 Emergence of diverse collective behaviors from local topological perception 01:00...
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In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen'sequations in Banach modules over a unital C~*-algebra.It is applie... Chun,Gil,PARK,... - 《数学学报(英文版)》 被引量: 101发表: 2004年 Torsion-free abelian groups of finite rank projective as modu...
To implement clustering, the multi-way data, viewed as tensors, are represented by the proposed tensor sparse and low-rank model to obtain its submodule representation, called a free module, which is finally used for spectral clustering. The proposed method extends the conventional subspace ...