ALL GORENSTEIN HEREDITARY RINGS ARE COHERENT
ALL GORENSTEIN HEREDITARY RINGS ARE COHERENT
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DOI：
10.1142/s0219498813501405
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发表时间：
2014-01
影响因子：
0.8
通讯作者：
Zenghui Gao;Fanggui Wang
中科院分区：
文献类型：
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作者：
Zenghui Gao;Fanggui Wang
环R称为Gorenstein遗传(G-遗传)，如果投射模的每个子模都是Gorenstein投射的(即Ggldim(R)≤1)。本文解决了Mahdou和Tamekkante在阿拉伯(强)Gorenstein(半)遗传环上提出的一个问题。J.Sci。Eng.36(2011)436]关于G-遗传环的相干性。证明了环R是Gorenstein半遗传环当且仅当投射模的每个有限生成子模都是Gorenstein投射模。作为这一结果的结果，我们得到每个G-遗传环R是凝聚的。
A ring R is called Gorenstein hereditary (G-hereditary) if every submodule of a projective module is Gorenstein projective (i.e. Ggldim(R) ≤ 1). In this paper, we settle a question raised by Mahdou and Tamekkante in [On (strongly) Gorenstein (semi)hereditary rings, Arab. J. Sci. Eng.36 (2011) 436] about the coherence of G-hereditary rings. It is shown that a ring R is Gorenstein semihereditary if and only if every finitely generated submodule of a projective module is Gorenstein projective. As a consequence of this result, we have that every G-hereditary ring R is coherent.