Event
01_1
| 제출번호(No.) | 0070 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Algebra (AL) |
| 영문제목 (Title(Eng.)) |
The complete decomposition on piecewise prime modules |
| 저자(Author(s)) |
Gangyong Lee1, S. Tariq Rizvi2 Chungnam National University1, The Ohio State University at Lima2 |
| 초록본문(Abstract) | The purpose of this talk is to further the study of quasi-Baer modules by investigating the structure of a special class of quasi-Baer modules. As a module theoretic analogue of a piecewise prime ring, we characterize a piecewise prime module (simply, a PWP module) via its endomorphism ring. We provide a complete decomposition theorem for a PWP module as a finite direct sum of endoprime modules, which play a role analogous to that of prime rings in the case of PWP rings. We also show that endoprime submodules are the building blocks of all PWP modules. A module $M$ is called \emph{endoprime} if every nonzero fully invariant submodule is faithful as a left module over its endomorphism ring, equivalently if $\mathbf{l}_S(N)=0$ for all $N \unlhd M$ where $S=\text{End}_R(M)$. We also obtained that every direct summand of a PWP module is a PWP module. It is shown that any direct sum of copies of a PWP module is always a PWP module. Consequently, every column finite matrix ring over a PWP ring is a PWP ring. \vspace{0.2cm} This is a joint work with S. Tariq Rizvi. |
| 분류기호 (MSC number(s)) |
16D70, 16S50 |
| 키워드(Keyword(s)) | quasi-Baer module, endoprime module, piecewise prime ring, piecewise prime module |
| 강연 형태 (Language of Session (Talk)) |
Korean |