On second submodules. (English) Zbl 1326.16001
Dougherty, Steven (ed.) et al., Noncommutative rings and their applications. International conference on noncommutative rings and their applications, Université d’Artois, Lens, France, July 1–4, 2013. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1032-2/pbk; 978-1-4704-2264-6/ebook). Contemporary Mathematics 634, 67-77 (2015).
Summary: 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.
For the entire collection see [Zbl 1310.16001].
For the entire collection see [Zbl 1310.16001].
MSC:
| 16D10 | General module theory in associative algebras |
| 16P60 | Chain conditions on annihilators and summands: Goldie-type conditions |
| 16N60 | Prime and semiprime associative rings |
| 16L30 | Noncommutative local and semilocal rings, perfect rings |
