Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 808 - 821 2020-04-02

On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings

Zhu ZHANMİN [1]


Let $R$ be a ring and $\mathscr{C}$ be a class of some finitely presented left $R$-modules. A left $R$-module $M$ is called $\mathscr{C}$-injective if Ext$^1_R(C, M)=0$ for every $C\in \mathscr{C}$; a left $R$-module $M$ is called $\mathscr{C}$-projective if ${\rm Ext}^1_R(M, E)=0$ for any $\mathscr{C}$-injective module $E$. $R$ is called left $\mathscr{C}$-coherent if every $C\in \mathscr{C}$ is 2-presented; $R$ is called left strongly $\mathscr{C}$-coherent, if whenever $0\rightarrow K\rightarrow P\rightarrow C\rightarrow 0$ is exact, where $C\in \mathscr{C}$ and $P$ is finitely generated projective, then $K$ is $\mathscr{C}$-projective; a ring $R$ is called left $\mathscr{C}$-semihereditary, if whenever $0\rightarrow K\rightarrow P\rightarrow C\rightarrow 0$ is exact, where $C\in \mathscr{C}$ , $P$ is finitely generated projective, then $K$ is projective. In this paper, we give some new characterizations and properties of left $\mathscr{C}$-coherent rings, left strongly $\mathscr{C}$-coherent rings and left $\mathscr{C}$-semihereditary rings.
C -coherent ring, strongly C -coherent ring, C -semihereditary ring
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Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0002-3131-3865
Yazar: Zhu ZHANMİN (Sorumlu Yazar)
Kurum: Jiaxing University
Ülke: China


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms624000, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {808 - 821}, doi = {10.15672/hujms.624000}, title = {On \$\\mathscr\{C\}\$-coherent rings, strongly \$\\mathscr\{C\}\$-coherent rings and \$\\mathscr\{C\}\$-semihereditary rings}, key = {cite}, author = {ZHANMİN, Zhu} }
APA ZHANMİN, Z . (2020). On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 808-821 . DOI: 10.15672/hujms.624000
MLA ZHANMİN, Z . "On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 808-821 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/624000>
Chicago ZHANMİN, Z . "On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 808-821
RIS TY - JOUR T1 - On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings AU - Zhu ZHANMİN Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.624000 DO - 10.15672/hujms.624000 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 808 EP - 821 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.624000 UR - https://doi.org/10.15672/hujms.624000 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings %A Zhu ZHANMİN %T On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.624000 %U 10.15672/hujms.624000
ISNAD ZHANMİN, Zhu . "On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 808-821 . https://doi.org/10.15672/hujms.624000
AMA ZHANMİN Z . On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 808-821.
Vancouver ZHANMİN Z . On $\mathscr{C}$-coherent rings, strongly $\mathscr{C}$-coherent rings and $\mathscr{C}$-semihereditary rings. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 821-808.