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 |
Nội dung
Basic Notions | 1 |
Singular and uniform modules | 29 |
The extending property | 55 |
Related Modules Extending | 92 |
Injectivity of Certain Modules | 136 |
Chain Conditions | 169 |
| 207 | |
| 223 | |
Ấn bản in khác - Xem tất cả
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
apply Assume called characterizations clear Clearly closed co-semisimple commutative consider contains continuous contradiction Corollary countably cr[M cyclic decomposition denote direct sum direct summand E-extending element essential submodule exact example exists extending module fact factor module finite uniform dimension following are equivalent follows fully invariant given gives hence hereditary homomorphic hypothesis idempotent implies indecomposable infinite injective injective module isomorphic Krull dimension left ideal left noetherian left non-singular left R-module left self-injective Lemma length locally noetherian M-generated M-injective M-injective hull M-projective M-singular module M/SocM monomorphism noetherian non-zero non-zero submodule Note obtain Obviously particular projective Proof proper properties Proposition prove Recall regular result ring satisfies self-projective semi-artinian semiprime semisimple semisimple module sequence simple simple module singular Sl-module socle SocM Suppose Theorem theory uniform modules uniform submodule uniserial zero