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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 143 - 154 (12page)
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Lomp [9] has studied finitely generated projective modules over semilocal rings. He obtained the following: finitely generated projective modules over semilocal
rings are semilocal. We shall give necessary and sufficient conditions for finitely generated
modules to be semilocal modules. By using a lifting property, we also give characterizations of right perfect (semiperfect) rings. Our main results can be summarized as follows:
(1) Let M be a finitely generated module. Then M has finite hollow dimension if and only if M is weakly supplemented if and only if M is semilocal.
(2) A ring R is right perfect if and only if every flat right R-module is lifting and every right R-module has a flat cover if and only if every quasi-projective right R-module is lifting.
(3) A ring R is semiperfect if and only if every finitely generated flat right R-module is lifting if and only if RR satisfies the lifting property for simple factor modules.
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참고문헌 (12)
참고문헌 신청
A. Amini / 2007 / On generalized perfect rings / Comm. Algebra 35 (3) : 953 ~ 963
C. Lomp / 1999 / On semilocal modules and rings / Comm. Algebra 27 (4) : 1921 ~ 1935
E. Mares / 1963 / Semiperfect modules / Math. Z 82 : 347 ~ 360
F. W. Anderson / 1992 / Rings and Categories of Modules, Springer-Verlag / Berlin-Heidelberg-New York
H. Bass / 1960 / Finitistic Dimension and Homological Generalization of Semiprimary Rings / Trans. Amer. Math 95 : 466 ~ 486
C. Lomp / 1999 / On semilocal modules and rings / Comm. Algebra 27 (4) : 1921 ~ 1935
E. Mares / 1963 / Semiperfect modules / Math. Z 82 : 347 ~ 360
F. W. Anderson / 1992 / Rings and Categories of Modules, Springer-Verlag / Berlin-Heidelberg-New York
H. Bass / 1960 / Finitistic Dimension and Homological Generalization of Semiprimary Rings / Trans. Amer. Math 95 : 466 ~ 486
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