Department of mathematics,jiaxing university,jiaxing,zhejiang province,china,314001
Abstract
Let $R$ be a ring, and let $n, d$ be non-negative integers. A right $R$-module $M$ is called $(n, d)$-projective if $Ext^{d+1}_R(M, A)=0$ for every $n$-copresented right $R$-module $A$. $R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted, it is called a right co-$(n,d)$-ring if every right $R$-module is $(n, d)$-projective. $R$ is called right $n$-cosemihereditary if every submodule of a projective right $R$-module is $(n, 0)$-projective, it is called a right $n$-V-ring if it is a right co-$(n,0)$-ring. Some properties of $(n, d)$-projective modules and $(n, d)$-projective dimensions of modules over $n$-cocoherent rings are studied. Certain characterizations of $n$-copresented modules, $(n, 0)$-projective modules, right $n$-cocoherent rings, right $n$-cosemihereditary rings, as well as right $n$-V-rings are given respectively.
Zhu, Z. (2014). $n$-cocoherent rings, $n$-cosemihereditary rings and $n$-V-rings. Bulletin of the Iranian Mathematical Society, 40(4), 809-822.
MLA
Z. Zhu. "$n$-cocoherent rings, $n$-cosemihereditary rings and $n$-V-rings". Bulletin of the Iranian Mathematical Society, 40, 4, 2014, 809-822.
HARVARD
Zhu, Z. (2014). '$n$-cocoherent rings, $n$-cosemihereditary rings and $n$-V-rings', Bulletin of the Iranian Mathematical Society, 40(4), pp. 809-822.
VANCOUVER
Zhu, Z. $n$-cocoherent rings, $n$-cosemihereditary rings and $n$-V-rings. Bulletin of the Iranian Mathematical Society, 2014; 40(4): 809-822.