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

A module M is called a D4-module if, whenever A and B are submodules of M with M = AB and f : AB is a homomorphism with Imf a direct summand of B, then Kerf is a direct summand of A. The class of D4-modules contains the class of D3-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 D3 iff M is D4. Also we prove that, over a prime PI-ring, for a divisible R-module X, X is direct projective (equivalently, it is Rickart) iff XX is D4. We determine some D3-modules and D4-modules over a discrete valuation ring, as well. We give some relevant examples. We also provide several examples on D3-modules and D4-modules via quivers.

中文翻译:

D3 模块 VS D4 模块 – 箭袋的应用

一个模块被称为D4-模块如果,无论何时一种是的子模块=一种F一种是与 Im 的同态F直接汇总,然后克尔F是直接总和一种. 类D4-modules 包含的类D3-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-模块这是循环子模块的直接和,是直接射影(等效地,它是半射影)iffD3 如果D4. 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XXD4. 我们确定一些D3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D3个模块和D通过 quivers 的 4 个模块。
更新日期:2020-10-06
down
wechat
bug