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- W2475806290 abstract "A real n -dimensional vector space is a unital module over the field of real numbers. The linear subspaces are submodules of this module, and the linear transformations are operator endomorphisms. If all the right ideals of the ring R are principal and R does not contain any divisors of zero, then every non-zero submodule of a free R-module will itself be a free R-module. Every Abelian group is a module over the ring of integers, and this ring is a principal ideal ring. Every non-zero subgroup of a free Abelian group is itself free. In a free Abelian group S of finite rank n the rank of every subgroup is finite and does not exceed n ." @default.
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- W2475806290 date "1965-01-01" @default.
- W2475806290 modified "2023-10-16" @default.
- W2475806290 title "OPERATOR GROUPS AND RINGS. MODULES. LINEAR ALGEBRAS" @default.
- W2475806290 doi "https://doi.org/10.1016/b978-0-08-010352-5.50008-1" @default.
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