On Second Submodules
Seçil Çeken, Mustafa Alkan · Contemporary mathematics - American Mathematical Society · 2015
Let R R be a ring with identity and M M be a unital right R R -module. A nonzero submodule N N of M M is called a second submodule if N N and all its nonzero homomorphic images have the same annihilator in R R . The second radical of a module M M is defined to be the sum of all second submodules of M 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.