当前位置:
X-MOL 学术
›
Glasg. Math. J.
›
论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
D3-MODULES VERSUS D4-MODULES – APPLICATIONS TO QUIVERS
Glasgow Mathematical Journal ( IF 0.5 ) Pub Date : 2020-10-06 , DOI: 10.1017/s0017089520000452 GABRIELLA D′ESTE , DERYA KESKİN TÜTÜNCÜ , RACHID TRIBAK
Glasgow Mathematical Journal ( IF 0.5 ) Pub Date : 2020-10-06 , DOI: 10.1017/s0017089520000452 GABRIELLA D′ESTE , DERYA KESKİN TÜTÜNCÜ , RACHID TRIBAK
A module M is called a D 4-module if, whenever A and B are submodules of M with M = A ⊕ B and f : A → B is a homomorphism with Imf a direct summand of B , then Kerf is a direct summand of A . The class of D 4-modules contains the class of D 3-modules, and hence the class of semi-projective modules, and so the class of Rickart modules. In this paper we prove that, over a commutative Dedekind domain R , for an R -module M which is a direct sum of cyclic submodules, M is direct projective (equivalently, it is semi-projective) iff M is D 3 iff M is D 4. Also we prove that, over a prime PI-ring, for a divisible R -module X , X is direct projective (equivalently, it is Rickart) iff X ⊕ X is D 4. We determine some D 3-modules and D 4-modules over a discrete valuation ring, as well. We give some relevant examples. We also provide several examples on D 3-modules and D 4-modules via quivers.
中文翻译:
D3 模块 VS D4 模块 – 箭袋的应用
一个模块米 被称为D 4-模块如果,无论何时一种 和乙 是的子模块米 和米 =一种 ⊕乙 和F :一种 →乙 是与 Im 的同态F 直接汇总乙 ,然后克尔F 是直接总和一种 . 类D 4-modules 包含的类D 3-模,因此是半射影模类,因此是 Rickart 模类。在本文中,我们证明了,在可交换的 Dedekind 域上R , 为R -模块米 这是循环子模块的直接和,米 是直接射影(等效地,它是半射影)iff米 是D 3 如果米 是D 4. 我们还证明,在素数 PI 环上,对于可整除R -模块X ,X 是直接射影(等价地,它是 Rickart)当且仅当X ⊕X 是D 4. 我们确定一些D 3个模块和D 离散估值环上的 4 个模块也是如此。我们举一些相关的例子。我们还提供了几个例子D 3个模块和D 通过 quivers 的 4 个模块。
更新日期:2020-10-06
中文翻译:
D3 模块 VS D4 模块 – 箭袋的应用
一个模块