On Second Submodules
International Conference on Noncommutative Rings and their Applications, Lens, France, 1 - 04 July 2013, vol.634, pp.67-77, (Full Text)
- Publication Type: Conference Paper / Full Text
- Volume: 634
- Doi Number: 10.1090/conm/634/12691
- City: Lens
- Country: France
- Page Numbers: pp.67-77
- Keywords: Second submodule, attached primes of a module, second radical of a module, hollow dimension, max property, DUAL NOTION, MODULES
- Akdeniz University Affiliated: Yes
Abstract
Let R be a ring with identity and M be a unital right R-module. A nonzero submodule N of M is called a second submodule if N and all its nonzero homomorphic images have the same annihilator in R. The second radical of a module M is defined to be the sum of all second submodules of M. In this paper we give some results concerning second submodules and attached primes of a module and we study the second radical of a module in some cases.