- PURE INJECTIVE REPRESENTATIONS OF QUIVERS
- PURE INJECTIVE REPRESENTATIONS OF QUIVERS
- ㆍ 저자명
- Hosseini. Esmaeil
- ㆍ 간행물명
- Bulletin of the Korean Mathematical Society
- ㆍ 권/호정보
- 2013년|50권 2호|pp.389-398 (10 pages)
- ㆍ 발행정보
- 대한수학회
- ㆍ 파일정보
- 정기간행물|ENG| PDF텍스트
- ㆍ 주제분야
- 기타
Let R be a ring and $mathcal{Q}$ be a quiver. In this paper we give another definition of purity in the category of quiver representations. Under such definition we prove that the class of all pure injective representations of $mathcal{Q}$ by R-modules is preenveloping. In case $mathcal{Q}$ is a left rooted semi-co-barren quiver and R is left Noetherian, we show that every cotorsion flat representation of $mathcal{Q}$ is pure injective. If, furthermore, R is $n$-perfect and $mathcal{F}$ is a flat representation $mathcal{Q}$, then the pure injective dimension of $mathcal{F}$ is at most $n$.