A Foundation of Torsion Theory for Modules Over General Rings
A Foundation of Torsion Theory for Modules Over General Rings
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DOI：
10.1017/s0027763000002099
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发表时间：
1960-08
影响因子：
0.8
通讯作者：
A. Hattori
中科院分区：
文献类型：
--
作者：
A. Hattori
当我们考虑非交换整环R上的模A时，通常的挠理论变得有些不足，因为R的零因子被忽略，而且A的挠元一般不形成子模。在本文中，我们将试图通过修改基本概念，如挠模，可除模等来弥补这些缺陷。
When we consider modules A over a ring R which is not a commutative integral domain, the usual torsion theory becomes somewhat inadequate, since zero-divisors of R are disregarded and since the torsion elements of A do not in general form a submodule. In this paper we shall try to remedy such defects by modifying the fundamental notions such as torsion modules, divisible modules, etc.