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- W4236289508 abstract "The lower radical of a module type . For a ring R with unit, the module type t ( R ) was defined in [6] as follows: t (0) = 0; t ( R ) = d if every free R -module has invariant rank; t ( R ) = ( c, k ) for integers c, k ≧ 1 if every free R -module of rank < c has invariant rank, while a free module of rank h ≧ c has rank h + nk for any integer n ≧ 0. The module types form a lattice under the ordering 0 < ( c, k ) < d and ( c', k' ) ≦ ( c, k ) if and only if c ' ≦ c and k' Ⅰ k . Two of the basic theorems on types are: A. [6; Theorem 2, p. 115] If R → R' is a unit-preserving homomorphism, then t ( R' )≦ t ( R ) ." @default.
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- W4236289508 date "1968-01-01" @default.
- W4236289508 modified "2023-09-25" @default.
- W4236289508 title "Type Radicals" @default.
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- W4236289508 doi "https://doi.org/10.1017/s0017089500000252" @default.
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