- Principally Small Injective Rings
- Principally Small Injective Rings
- ㆍ 저자명
- Xiang. Yueming
- ㆍ 간행물명
- Kyungpook mathematical journal
- ㆍ 권/호정보
- 2011년|51권 2호|pp.177-185 (9 pages)
- ㆍ 발행정보
- 경북대학교 자연과학대학 수학과
- ㆍ 파일정보
- 정기간행물|ENG| PDF텍스트
- ㆍ 주제분야
- 기타
A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ${ eq}$ = R. A right R-module M is called PS-injective if every R-homomorphism f : aR ${ ightarrow}$ M for every principally small right ideal aR can be extended to R ${ ightarrow}$ M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well.