2-Absorbing and Weakly 2-Absorbing Elements in Multiplicative Lattices

φ-Prime and φ-Primary Elements in Lattice Modules

“…According to [9], a proper element p ∈ L is said to be almost prime if for all a, b ∈ L, ab p and ab p 2 implies either a p or b p and according to [15], a proper element p ∈ L is said to be almost primary if for all a, b ∈ L, ab p and ab p 2 implies either a p or b √ p. Further study on almost prime and almost primary elements of a multiplicative lattice L is seen in [16], [5] and [4]. According to [12], a proper element q ∈ L is said to be 2-absorbing if for all a, b, c ∈ L, abc q implies either ab q or bc q or ca q. According to [18], a proper element q ∈ L is said to be 2-absorbing primary if for all a, b, c ∈ L, abc q implies either ab q or bc √ q or ca √ q.…”

Absorbing Elements in Lattice Modules

“…al. in [11] while the study of n-absorbing elements and weakly n-absorbing elements was done by S. Ballal et. al.…”

“…According to [11], a proper element q ∈ L is said to be a 2-absorbing element if for every a, b, c ∈ L; abc q implies either ab q or bc q or ca q and a proper element q ∈ L is said to be a weakly 2-absorbing element if for every a, b, c ∈ L; 0 = abc q implies either ab q or bc q or ca q. Obviously a prime element of L is a 1-absorbing element and a weakly prime element of L is a weakly 1-absorbing element.…”

On generalization of prime, weakly prime and almost prime elements in multiplicative lattices

“…al. [8] introduced and studied the concepts of 2-absorbing and weakly 2-absorbing elements in C-lattices as an extension of 2-absorbing ideals and weakly 2-absorbing ideals of commutative rings. Weakly prime elements and almost prime elements have been studied by Fethi Ç allialp and C. Jayaram [5] as an extension of weakly prime ideals and almost prime ideals of commutative rings.…”