On disjoint sets of natural classes

摘要

An M-natural class is any subclass of sigmaM which is closed under (1) submodules, (2) isomorphic copies, (3) direct sums and (4) M-injective envelopes. Let L be any set of pairwise disjoint M-natural classes. We define the L-dimension of an R-module and examine how finite L-dimension is related to certain-injectivity conditions in sigmaM. We also define a L-chain and relate ACC on L-chains again to certain injectivity conditions. References: 3