منابع مشابه
Linear Algebra over a Ring
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with coefficients in R. In the case when the ring R is a field, every pair is equivalent to a homogeneous system. Using the formal matrix calculus, two alternate pr...
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Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
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Suppose that F is a number field, with ring of integers OF . Let ` denote an odd prime and let R = OF [1/`]. In [3], the author and W.Dwyer gave an explicit conjectural computation of the mod ` cohomology of the infinite general linear group GLR. Here is the quickest and simplest statement of the conjecture (all homology and cohomology groups have Z/` coefficients): let U denote the infinite un...
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In this paper we first examine the computational complexity of the problem LCON defined as follows: given a matrix A and a column vector b over Z, determine if Ax = b is a feasible system of linear equations over Zq. Here q is also given as part of the input by its prime factorization q = p1 1 p2 2 . . . p ek k , such that each p ei i is tiny (i.e. given in unary). In [MC87] an NC algorithm is ...
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ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2006
ISSN: 1015-8634
DOI: 10.4134/bkms.2006.43.3.619