Vector Spaces, Modules over Chinese Rings, and Monoids as Unions of Proper Subobjects
نویسنده
چکیده
Given a vector space V over a field (of size at least 1), we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover V . If V is a finite set, this is related to the problem of partitioning V into subspaces. We also consider the analogous problem (involving proper subobjects only) for direct sums of cyclic monoids, cyclic groups, or cyclic modules over various classes of commutative rings. 1. Subspaces of finite codimension in vector spaces 1.
منابع مشابه
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تاریخ انتشار 2009