2 K, R, Goodearl and A. K, Boyle by maximality of H. Consequently Z(C/H) = 0 and so H e L*(C), whence K ^ H, Therefore A ^ K. e Conversely, let M e L*(C) such that A ^ M, and note that K S M. Observing that M/A is singular, we see that M/K is singular also, whence M/K ^ Z(C/K) = 0. Therefore M = K. DEFINITION, Given any module A and any cardinal * (finite or infinite), we use oA to denote the direct sum of ot copies of A. DEFINITION, A module A is subisomprphic to a module B, written A B, provided A is isomorphic to a submodule of B, THEQHEM 1,2, [2, Theorem] If A and B are infective modules such that A B and B A, then A 2-B. DEFINITION, For any ring R, we use 71(H) to denote the full subcategory of Mod-R generated by all nonsingular infective right R-modules, Clearly 7?(R) is an additive category with arbitrary products and finite coproducts. The following proposition identifies subobjects in 7KR). PROPOSITION 1.5, Let C e 7?(R), and let A be any submodule of C, Then the following conditions are equivalent: (a) A e 7J(R). (b) A e L*(C). (c) A is a closed submodule of C. (d) A is a direct summand of C. Proof, (c) * * (d) follows from the injectivity of C, and (d) =* (a) is clear.
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