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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2011.1
- 수록면
- 177 - 185 (9page)
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A right ideal I of a ring R is small in case for every proper right ideal K of R, K ＋ I ≠ R. A right R-module M is called PS-injective if every R-homomorphism f : aR → M for every principally small right ideal aR can be extended to R → 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.
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참고문헌 (12)
참고문헌 신청
F. W. Anderson / 1974 / Rings and Categories of Modules / Springer-Verlag
L. Shen / 2006 / New characterizations of quasi-Frobenius rings / Comm. Al-gebra 34 : 2157 ~ 2165
L. V. Thuyet / 2009 / On small injective rings and modules / J. Algebra and Its Appl 8 : 379 ~ 387
M. F. Yousif / 2004 / FP-injective, simple-injective and quasi-Frobenius rings / Comm. Algebra 32 : 2273 ~ 2285
M. Harada / 1982 / Self mini-injective rings / Osaka J. Math 19 : 587 ~ 597
L. Shen / 2006 / New characterizations of quasi-Frobenius rings / Comm. Al-gebra 34 : 2157 ~ 2165
L. V. Thuyet / 2009 / On small injective rings and modules / J. Algebra and Its Appl 8 : 379 ~ 387
M. F. Yousif / 2004 / FP-injective, simple-injective and quasi-Frobenius rings / Comm. Algebra 32 : 2273 ~ 2285
M. Harada / 1982 / Self mini-injective rings / Osaka J. Math 19 : 587 ~ 597
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