On almost generalized 2-absorbing and weakly almost generalized 2-absorbing structures

Sirawich Chinwarakorn, Sajee Pianskool
2015 ScienceAsia  
In this paper, we define almost generalized 2-absorbing submodules (ideals) and weakly almost generalized 2-absorbing submodules (ideals). These are generalizations of the 2-absorbing and weakly 2-absorbing submodules (ideals) defined by Badawi and Darani. Their properties are investigated. KEYWORDS: submodules , c ∈ R and abc ∈ I (0 = abc ∈ I), then ac ∈ I or bc ∈ I or ab ∈ I. Definition 3 [Ref. 4] A proper submodule N of M is called a primary (weakly primary) submodule of M if whenever r ∈ R,
more » ... if whenever r ∈ R, m ∈ M and r m ∈ N (0 = r m ∈ N ), then m ∈ N or r n ∈ (N : M ) for some n ∈ . Definition 4 A proper ideal P of R is said to be a primary (weakly primary) ideal if whenever a, b ∈ R and ab ∈ P (0 = ab ∈ P), then a ∈ P or b n ∈ P for some n ∈ . www.scienceasia.org
doi:10.2306/scienceasia1513-1874.2015.41.064 fatcat:wiglnrziajclhc2u7luorcbmia