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Let $(RDTF,M)$ be a Milnor square. In this paper, it is proved that $R$ is a $\mathcal{C}$-hereditary domain if and only if both $D$ and $T$ are $\mathcal{C}$-hereditary domains; $R$ is an almost perfect domain if and only if $D$ is a field and $T$ is an almost perfect domain; $R$ is a Matlis domain if and only if $T$ is a Matlis domain. Furthermore, to give a negative answer to Lee$^,$s question, we construct a counter example which is a $\mathcal{C}$-hereditary domain $R$ with $w.gl.\dim(R)=\infty$.
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참고문헌 (14)
참고문헌 신청
H. Bass / 1960 / Finitistic dimension and a homological generalization of semi-primary rings / Trans. Amer. Math. Soc. 95:466~488
S. Bazzoni / 2002 / Strongly flat covers / J. London Math. Soc. (2) 66(2):276~294
S. Bazzoni / 2003 / Almost perfect domains / Colloq. Math. 95(2):285~301
E. Enochs / 1984 / Flat covers and flat cotorsion modules / Proc. Amer. Math. Soc. 92(2):179~184
E. E. Enochs / 2005 / Dualizing modules and n-perfect rings / Proc. Edinb. Math. Soc. 48(1):75~90
S. Bazzoni / 2002 / Strongly flat covers / J. London Math. Soc. (2) 66(2):276~294
S. Bazzoni / 2003 / Almost perfect domains / Colloq. Math. 95(2):285~301
E. Enochs / 1984 / Flat covers and flat cotorsion modules / Proc. Amer. Math. Soc. 92(2):179~184
E. E. Enochs / 2005 / Dualizing modules and n-perfect rings / Proc. Edinb. Math. Soc. 48(1):75~90
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