Extending ModulesRoutledge, 22 thg 1, 2019 - 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 |
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Extending Modules Nguyen Viet Dung,Dinh Van Huynh,P F Smith,Robert Wisbauer Xem trước bị giới hạn - 1994 |
Thuật ngữ và cụm từ thông dụng
ACC on essential ACC on left Algebra Assume characterizations contains a non-zero contradiction Corollary countably cyclic left R-module cyclic module cyclic subfactor cyclic submodule decomposition denote direct sum direct summand endomorphism rings EndR(M essential extension essential left ideal essential submodule exists extending module factor module finite direct sum finite uniform dimension finitely cogenerated finitely generated module finitely generated submodule following are equivalent GCO-module hence HomR idempotent implies indecomposable infinite injective module isomorphic 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 modules M/Soc Math maximal submodule monomorphism noetherian module non-zero submodule projective module Proof properties quotient ring R-Mod semiperfect semiprime semisimple module SI-module simple module Soc RR sum of uniform Suppose Ʃ-extending Theorem uniform modules uniform submodule uniserial zero ZM(M