Extending ModulesCRC Press, 30 thg 11, 1994 - 248 trang Module theory is an important tool for many different branches of mathematics, as well as being an interesting subject in its own right. Within module theory, the concept of injective modules is particularly important. Extending modules form a natural class of modules which is more general than the class of injective modules but retains many of its desirable properties. This book gathers together for the first time in one place recent work on extending modules. It is aimed at anyone with a basic knowledge of ring and module theory. |
Ấn bản in khác - Xem tất cả
Thuật ngữ và cụm từ thông dụng
ACC on essential ACC on left Assume contains a non-zero contradiction Corollary countably cyclic left R-module cyclic subfactor cyclic submodule decomposition denote direct sum direct summand E-extending End R(M endomorphism ring essential extension essential left ideal essential submodule exists extending module factor module finite direct sum finite uniform dimension finitely cogenerated finitely generated submodule following are equivalent GCO-module hence HomŔ(M idempotent implies indecomposable infinite injective module isomorphic Kdim Krull dimension left and right left annihilators left artinian left ideal left noetherian left non-singular left quotient ring left semisimple left SI-ring left socle Lemma locally noetherian M-generated M-injective hull M-projective M-singular module M/Soc M₁ maximal left maximal submodule module in o[M monomorphism morphism N₁ noetherian module non-zero submodule projective module Proof properties quotient ring R-Mod semiperfect semiprime semisimple module SI-module simple module Soc RR subfactor sum of uniform Suppose Theorem udim uniform modules uniform submodule uniserial