|
|||||
|
|
Generalization of Nilpotency of Ring Elements to Module Elements |
|
| Authors: | David Ssevviiri Nico Groenewald |
| Institution: | 1. Department of Mathematics , Makerere University , Kampala , Uganda ssevviiri@math.mak.ac.ug;3. Department of Mathematics and Applied Mathematics , Nelson Mandela Metropolitan University , Port Elizabeth , South Africa |
| Abstract: | We define nilpotent and strongly nilpotent elements of a module M and show that the set 𝒩 s (M) of all strongly nilpotent elements of M over a commutative unital ring R coincides with the classical prime radical β cl (M) the intersection of all classical prime submodules of M. |
| Keywords: | Classical prime submodules Nilpotent elements of modules Strongly nilpotent elements of modules |