A Foundation of Torsion Theory for Modules Over General Rings
- 1 August 1960
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 17, 147-158
- https://doi.org/10.1017/s0027763000002099
Abstract
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.Keywords
This publication has 3 references indexed in Scilit:
- Homological dimension in local ringsTransactions of the American Mathematical Society, 1957
- On some characteristic properties of quasi-Frobenius and regular ringsProceedings of the American Mathematical Society, 1954
- On Regular RingsProceedings of the National Academy of Sciences, 1936