LetRbe a commutative ring with identity,Qbe a prime ideal ofRandFbe a freeR-module of finite rank. In this paper, we use hypergraphs to give a full characterization of prime submodules ofF. Also we define a hypergraphPHQ(F)called the prime submodules hypergraph ofFwith respect toQand use ...
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...
On Stably Free Modules 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......
A new submodule clustering method via sparse and low-rank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic structures, e.g., image data kept as matrices. To implem...
We present the state-of-the-art on maximum symmetric tensor rank, for each given dimension and order. After a general discussion on the interplay between symmetric tensors, polynomials and divided powers, we introduce the technical environment and the me
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Twitter Google Share on Facebook (Mil.)the rank or line of a body of troops which is in the rear, or last in order. See also:Rear Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co. Want to thank TFD for its existence?Tell a friend about us, add a li...
The RANK Function is categorized as an Excel Statistical function. The function returns the statistical rank of a given value within a supplied array of values.
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